Journal articles: 'Reaction-Diffusion Network Model'

1

Wang, Ling, and Hongyong Zhao. "Synchronized stability in a reaction–diffusion neural network model." Physics Letters A 378, no. 48 (November 2014): 3586–99. http://dx.doi.org/10.1016/j.physleta.2014.10.019.

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Ji, Yansu, and Jianwei Shen. "Turing Instability of Brusselator in the Reaction-Diffusion Network." Complexity 2020 (October 5, 2020): 1–12. http://dx.doi.org/10.1155/2020/1572743.

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Turing instability constitutes a universal paradigm for the spontaneous generation of spatially organized patterns, especially in a chemical reaction. In this paper, we investigated the pattern dynamics of Brusselator from the view of complex networks and considered the interaction between diffusion and reaction in the random network. After a detailed theoretical analysis, we obtained the approximate instability region about the diffusion coefficient and the connection probability of the random network. In the meantime, we also obtained the critical condition of Turing instability in the network-organized system and found that how the network connection probability and diffusion coefficient affect the reaction-diffusion system of the Brusselator model. In the end, the reason for arising of Turing instability in the Brusselator with the random network was explained. Numerical simulation verified the theoretical results.

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Zhao, Hongyong, and Linhe Zhu. "Dynamic Analysis of a Reaction–Diffusion Rumor Propagation Model." International Journal of Bifurcation and Chaos 26, no. 06 (June 15, 2016): 1650101. http://dx.doi.org/10.1142/s0218127416501017.

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The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

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Kumar, Dinesh, Jatin Gupta, and Soumyendu Raha. "Partitioning a reaction–diffusion ecological network for dynamic stability." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2223 (March 2019): 20180524. http://dx.doi.org/10.1098/rspa.2018.0524.

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The loss of dispersal connections between habitat patches may destabilize populations in a patched ecological network. This work studies the stability of populations when one or more communication links is removed. An example is finding the alignment of a highway through a patched forest containing a network of metapopulations in the patches. This problem is modelled as that of finding a stable cut of the graph induced by the metapopulations network, where nodes represent the habitat patches and the weighted edges model the dispersal between habitat patches. A reaction–diffusion system on the graph models the dynamics of the predator–prey system over the patched ecological network. The graph Laplacian's Fiedler value, which indicates the well-connectedness of the graph, is shown to affect the stability of the metapopulations. We show that, when the Fiedler value is sufficiently large, the removal of edges without destabilizing the dynamics of the network is possible. We give an exhaustive graph partitioning procedure, which is suitable for smaller networks and uses the criterion for both the local and global stability of populations in partitioned networks. A heuristic graph bisection algorithm that preserves the preassigned lower bound for the Fiedler value is proposed for larger networks and is illustrated with examples.

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Doremus, R. H. "Diffusion of water in crystalline and glassy oxides: Diffusion–reaction model." Journal of Materials Research 14, no. 9 (September 1999): 3754–58. http://dx.doi.org/10.1557/jmr.1999.0508.

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Diffusion of water in oxides is modeled as resulting from the solution and diffusion of molecular water in the oxide. This dissolved water can react and exchange with the oxide network to form immobile OH groups and different hydrogen and oxygen isotopes in the oxide. The model agrees with many experiments on water diffusion in oxides. The activation energy for diffusion of water in oxides correlates with the structural openness of the oxide, suggesting that molecular water is the diffusing species.

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BANERJEE, SUBHASIS, SHRESTHA BASU MALLICK, and INDRANI BOSE. "REACTION–DIFFUSION PROCESSES ON RANDOM AND SCALE-FREE NETWORKS." International Journal of Modern Physics C 15, no. 08 (October 2004): 1075–86. http://dx.doi.org/10.1142/s0129183104006534.

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We study the discrete Gierer–Meinhardt model of reaction–diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.

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Smith, Stephen, and Neil Dalchau. "Model reduction enables Turing instability analysis of large reaction–diffusion models." Journal of The Royal Society Interface 15, no. 140 (March 2018): 20170805. http://dx.doi.org/10.1098/rsif.2017.0805.

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Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted to systems of two or three chemical species, for which equations are tractable. However, when models seek to combine descriptions of intercellular signal diffusion and intracellular biochemistry, plausible genetic networks can consist of dozens of interacting species. In this paper, we suggest a method for reducing large biochemical systems that relies on removing the non-diffusible species, leaving only the diffusibles in the model. Such model reduction enables analysis to be conducted on a smaller number of differential equations. We provide conditions to guarantee that the full system forms patterns if the reduced system does, and vice versa. We confirm our technique with three examples: the Brusselator, an example proposed by Turing, and a biochemically plausible patterning system consisting of 17 species. These examples show that our method significantly simplifies the study of pattern formation in large systems where several species can be considered immobile.

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Slavova, Angela, and Ronald Tetzlaff. "Edge of chaos in reaction diffusion CNN model." Open Mathematics 15, no. 1 (February 2, 2017): 21–29. http://dx.doi.org/10.1515/math-2017-0002.

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Abstract In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic patterns in the RD-CNN model with memristor coupling.

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Liu, Chen, Shupeng Gao, Mingrui Song, Yue Bai, Lili Chang, and Zhen Wang. "Optimal control of the reaction–diffusion process on directed networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063115. http://dx.doi.org/10.1063/5.0087855.

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Reaction–diffusion processes organized in networks have attracted much interest in recent years due to their applications across a wide range of disciplines. As one type of most studied solutions of reaction–diffusion systems, patterns broadly exist and are observed from nature to human society. So far, the theory of pattern formation has made significant advances, among which a novel class of instability, presented as wave patterns, has been found in directed networks. Such wave patterns have been proved fruitful but significantly affected by the underlying network topology, and even small topological perturbations can destroy the patterns. Therefore, methods that can eliminate the influence of network topology changes on wave patterns are needed but remain uncharted. Here, we propose an optimal control framework to steer the system generating target wave patterns regardless of the topological disturbances. Taking the Brusselator model, a widely investigated reaction–diffusion model, as an example, numerical experiments demonstrate our framework’s effectiveness and robustness. Moreover, our framework is generally applicable, with minor adjustments, to other systems that differential equations can depict.

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Liu, Chen, Shupeng Gao, Mingrui Song, Yue Bai, Lili Chang, and Zhen Wang. "Optimal control of the reaction–diffusion process on directed networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063115. http://dx.doi.org/10.1063/5.0087855.

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Reaction–diffusion processes organized in networks have attracted much interest in recent years due to their applications across a wide range of disciplines. As one type of most studied solutions of reaction–diffusion systems, patterns broadly exist and are observed from nature to human society. So far, the theory of pattern formation has made significant advances, among which a novel class of instability, presented as wave patterns, has been found in directed networks. Such wave patterns have been proved fruitful but significantly affected by the underlying network topology, and even small topological perturbations can destroy the patterns. Therefore, methods that can eliminate the influence of network topology changes on wave patterns are needed but remain uncharted. Here, we propose an optimal control framework to steer the system generating target wave patterns regardless of the topological disturbances. Taking the Brusselator model, a widely investigated reaction–diffusion model, as an example, numerical experiments demonstrate our framework’s effectiveness and robustness. Moreover, our framework is generally applicable, with minor adjustments, to other systems that differential equations can depict.

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11

ZHONG, YONGMIN, BIJAN SHIRINZADEH, and JULIAN SMITH. "REACTION-DIFFUSION BASED DEFORMABLE OBJECT SIMULATION." International Journal of Image and Graphics 08, no. 02 (April 2008): 265–80. http://dx.doi.org/10.1142/s0219467808003088.

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This paper presents a new methodology to simulate soft object deformation by drawing an analogy between reaction-diffusion and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by the principle of reaction-diffusion. An improved reaction-diffusion model is developed to propagate the energy generated by the external force. A three-layer cellular neural network is established to solve the reaction-diffusion model for real-time simulation of soft object deformation. A material flux based method is presented to derive internal forces from the potential energy distribution established by the reaction-diffusion model. The proposed methodology not only accommodates isotropic, anisotropic and inhomogeneous deformations by simple modification of diffusion coefficients, but it also accepts large-range deformations.

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12

Wang, Suxia. "Hopf Bifurcation for a FitzHugh–Nagumo Model with Time Delay in a Network." Complexity 2021 (July 8, 2021): 1–9. http://dx.doi.org/10.1155/2021/9931662.

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A reaction diffusion system is used to study the interaction between species in a population dynamic system. It is not only used in a population dynamic system with the diffusion phenomenon but also used in physical chemistry, medicine, and animal and plant protection. It has been studied by more and more scholars in recent years. The FitzHugh–Nagumo model is one of the most famous reaction-diffusion models. This article takes a deeper look at a FitzHugh–Nagumo model in a network with time delay. Firstly, we studied the linear stability of the equilibrium, then the existence of Hopf bifurcation is given, and finally, the stability of the Hopf bifurcation is introduced.

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Liu, Hung-Yi, and Chien-Chi Lin. "A Diffusion-Reaction Model for Predicting Enzyme-Mediated Dynamic Hydrogel Stiffening." Gels 5, no. 1 (March 13, 2019): 17. http://dx.doi.org/10.3390/gels5010017.

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Hydrogels with spatiotemporally tunable mechanical properties have been increasingly employed for studying the impact of tissue mechanics on cell fate processes. These dynamic hydrogels are particularly suitable for recapitulating the temporal stiffening of a tumor microenvironment. To this end, we have reported an enzyme-mediated stiffening hydrogel system where tyrosinase (Tyrase) was used to stiffen orthogonally crosslinked cell-laden hydrogels. Herein, a mathematical model was proposed to describe enzyme diffusion and reaction within a highly swollen gel network, and to elucidate the critical factors affecting the degree of gel stiffening. Briefly, Fick’s second law of diffusion was used to predict enzyme diffusion in a swollen poly(ethylene glycol) (PEG)-peptide hydrogel, whereas the Michaelis–Menten model was employed for estimating the extent of enzyme-mediated secondary crosslinking. To experimentally validate model predictions, we designed a hydrogel system composed of 8-arm PEG-norbornene (PEG8NB) and bis-cysteine containing peptide crosslinker. Hydrogel was crosslinked in a channel slide that permitted one-dimensional diffusion of Tyrase. Model predictions and experimental results suggested that an increasing network crosslinking during stiffening process did not significantly affect enzyme diffusion. Rather, diffusion path length and the time of enzyme incubation were more critical in determining the distribution of Tyrase and the formation of additional crosslinks in the hydrogel network. Finally, we demonstrated that the enzyme-stiffened hydrogels exhibited elastic properties similar to other chemically crosslinked hydrogels. This study provides a better mechanistic understanding regarding the process of enzyme-mediated dynamic stiffening of hydrogels.

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Li, Jingjing, and Ningkui Sun. "Dynamical behavior of solutions of a reaction–diffusion model in river network." Nonlinear Analysis: Real World Applications 75 (February 2024): 103989. http://dx.doi.org/10.1016/j.nonrwa.2023.103989.

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15

Em, Phan Van Long. "Indentical synchronization in complete networks of reaction-diffusion equations of FitzHugh-Nagumo." ENGINEERING AND TECHNOLOGY 8, no. 2 (June 4, 2020): 45–53. http://dx.doi.org/10.46223/hcmcoujs.tech.en.8.2.346.2018.

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Synchronization is a ubiquitous feature in many natural systems and nonlinear science. This paper studies the synchronization in complete network consisting of n nodes. Each node is connected to all other nodes by linear coupling and represented by a reaction-diffusion system of FitzHugh-Nagumo type which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, the author seeks a sufficient condition on the coupling strength to achieve synchronization. The result shows that the more easily the nodes synchronize, the bigger the degrees of the networks. Based on this consequence, the author will test the theoretical result numerically to see if there is a compromise.

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Martins, António, Carlos H. Braga, and Teresa M. Mata. "Macroscopic and Microscopic Effects in Diffusion and Reaction in Catalyst Porous Particles." Defect and Diffusion Forum 283-286 (March 2009): 388–93. http://dx.doi.org/10.4028/www.scientific.net/ddf.283-286.388.

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This article presents and discusses a network model to describe and predict the behaviour and performance of catalyst particles. The differences and advantages of this approach when compared to the continuous models currently used in practice are highlighted and critically assessed. The local structure of the catalyst particle is modelled using a three dimensional network model made up of cylindrical pores and nodes of negligible volume. In the pores a homogenous first-order reaction takes place, coupled with the diffusion. For steady state conditions the concentration field can be obtained solving a sparse linear system of equations, obtained by solving the mass balance equations written for the network nodes and using the concentration profile in the network pores. The influence of the boundary conditions and the network sizes was investigated, showing the results in particular that the nature of the boundary conditions can have a profound impact in the predictions of the model.

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Carletti, Timoteo, and Riccardo Muolo. "Finite propagation enhances Turing patterns in reaction–diffusion networked systems." Journal of Physics: Complexity 2, no. 4 (October 19, 2021): 045004. http://dx.doi.org/10.1088/2632-072x/ac2cdb.

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Abstract We hereby develop the theory of Turing instability for reaction–diffusion systems defined on complex networks assuming finite propagation. Extending to networked systems the framework introduced by Cattaneo in the 40s, we remove the unphysical assumption of infinite propagation velocity holding for reaction–diffusion systems, thus allowing to propose a novel view on the fine tuning issue and on existing experiments. We analytically prove that Turing instability, stationary or wave-like, emerges for a much broader set of conditions, e.g., once the activator diffuses faster than the inhibitor or even in the case of inhibitor–inhibitor systems, overcoming thus the classical Turing framework. Analytical results are compared to direct simulations made on the FitzHugh–Nagumo model, extended to the relativistic reaction–diffusion framework with a complex network as substrate for the dynamics.

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Huang, Guo Rui, Yan Mou Zhan, Xu Cheng, Hua Qiang Wu, and Hao Li. "The Study of Artificial Endocrine Network Model and its Application in Robot Navigation Control." Advanced Materials Research 341-342 (September 2011): 685–89. http://dx.doi.org/10.4028/www.scientific.net/amr.341-342.685.

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Relative stability of the internal environment is the basis for the body’s all intelligent activities, and the endocrine system plays an irreplaceable role in maintaining that stability. Based on the self-organization mechanism of the hormone reaction diffusion in the endocrine system, this paper presents the artificial endocrine network model and the model-based learning algorithm. The model depends on the diffusion of artificial hormones and its reaction with suitable receptors to achieve the dynamic balance control of the artificial endocrine network. In order to validate the feasibility of the model and algorithm, this paper makes a simulation experiment of robotic navigation control, whose results also show that the model and its algorithm has good adaptive solving ability.

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Schmitt, Oliver, Christian Nitzsche, Peter Eipert, Vishnu Prathapan, Marc-Thorsten Hütt, and Claus Hilgetag. "Reaction-diffusion models in weighted and directed connectomes." PLOS Computational Biology 18, no. 10 (October 28, 2022): e1010507. http://dx.doi.org/10.1371/journal.pcbi.1010507.

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Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances. Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway. In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

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Shao, Shuxiang, and Bo Du. "Global Asymptotic Stability of Competitive Neural Networks with Reaction-Diffusion Terms and Mixed Delays." Symmetry 14, no. 11 (October 22, 2022): 2224. http://dx.doi.org/10.3390/sym14112224.

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In this article, a new competitive neural network (CNN) with reaction-diffusion terms and mixed delays is proposed. Because this network system contains reaction-diffusion terms, it belongs to a partial differential system, which is different from the existing classic CNNs. First, taking into account the spatial diffusion effect, we introduce spatial diffusion for CNNs. Furthermore, since the time delay has an essential influence on the properties of the system, we introduce mixed delays including time-varying discrete delays and distributed delays for CNNs. By constructing suitable Lyapunov–Krasovskii functionals and virtue of the theories of delayed partial differential equations, we study the global asymptotic stability for the considered system. The effectiveness and correctness of the proposed CNN model with reaction-diffusion terms and mixed delays are verified by an example. Finally, some discussion and conclusions for recent developments of CNNs are given.

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Zhou, Lufang, Miguel A. Aon, Tabish Almas, Sonia Cortassa, Raimond L. Winslow, and Brian O'Rourke. "A Reaction-Diffusion Model of ROS-Induced ROS Release in a Mitochondrial Network." PLoS Computational Biology 6, no. 1 (January 29, 2010): e1000657. http://dx.doi.org/10.1371/journal.pcbi.1000657.

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SU, YONGMEI, and LEQUAN MIN. "CELLULAR NEURAL NETWORK MODELS OF GROWTH AND IMMUNE OF EFFECTOR CELLS RESPONSE TO CANCER." International Journal of Modern Physics C 17, no. 02 (February 2006): 223–33. http://dx.doi.org/10.1142/s0129183106008790.

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Four reaction-diffusion cellular neural network (R-D CNN) models are set up based on the differential equation models for the growths of effector cells and cancer cells, and the model of the immune response to cancer proposed by Allison et al. The CNN models have different reaction-diffusion coefficients and coupling parameters. The R-D CNN models may provide possible quantitative interpretations, and are good in agreement with the in vitro experiment data reported by Allison et al.

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Rao, Ruofeng, and Shouming Zhong. "Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory." Complexity 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/6292597.

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This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

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Piazza, Stefania, Mariacrocetta Sambito, and Gabriele Freni. "Analysis of diffusion and dispersion processes in water distribution networks through the use of the Péclet number threshold." IOP Conference Series: Earth and Environmental Science 1136, no. 1 (January 1, 2023): 012049. http://dx.doi.org/10.1088/1755-1315/1136/1/012049.

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Abstract To model the water quality within the distribution networks, simplified models are used (such as EPANET), which use an advective-reactive approach and neglect relevant phenomena, such as diffusion and dispersion, for low values of the Reynolds number. Although valid in the presence of a purely turbulent flow regime, as they do not produce substantial modelling errors, these simplifications are not applicable equally to all distribution networks. Therefore, the present study defines a threshold of the Péclet number, which relates the effectiveness of mass transport by advection with the effectiveness of mass transport by dispersion or diffusion, in order to establish a priori the behaviour of the water distribution network and find the most suitable model to use. The numerical analysis was applied to a real case study (network of Oreto-Stazione) using EPANET advective model and EPANET-DDR (Dynamic-Dispersion-Reaction) model, developed by the authors.

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Chen, Sichen, Nicolas J.-B. Brunel, Xin Yang, and Xinping Cui. "Learning Interactions in Reaction Diffusion Equations by Neural Networks." Entropy 25, no. 3 (March 11, 2023): 489. http://dx.doi.org/10.3390/e25030489.

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Partial differential equations are common models in biology for predicting and explaining complex behaviors. Nevertheless, deriving the equations and estimating the corresponding parameters remains challenging from data. In particular, the fine description of the interactions between species requires care for taking into account various regimes such as saturation effects. We apply a method based on neural networks to discover the underlying PDE systems, which involve fractional terms and may also contain integration terms based on observed data. Our proposed framework, called Frac-PDE-Net, adapts the PDE-Net 2.0 by adding layers that are designed to learn fractional and integration terms. The key technical challenge of this task is the identifiability issue. More precisely, one needs to identify the main terms and combine similar terms among a huge number of candidates in fractional form generated by the neural network scheme due to the division operation. In order to overcome this barrier, we set up certain assumptions according to realistic biological behavior. Additionally, we use an L2-norm based term selection criterion and the sparse regression to obtain a parsimonious model. It turns out that the method of Frac-PDE-Net is capable of recovering the main terms with accurate coefficients, allowing for effective long term prediction. We demonstrate the interest of the method on a biological PDE model proposed to study the pollen tube growth problem.

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Phan, Van Long Em. "Synchronization in complete networks of reaction-diffusion equations of FitzHugh-Nagumo type with nonlinear coupling." Can Tho University Journal of Science 13, no. 2 (July 19, 2021): 43–51. http://dx.doi.org/10.22144/ctu.jen.2021.029.

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The synchronization in complete network consisting of nodes is studied in this paper. Each node is connected to all other ones by nonlinear coupling and is represented by a reaction-diffusion system of FitzHugh-Nagumo type which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, the sufficient condition on the coupling strength to achieve the synchronization is found. The result shows that the networks with bigger in-degrees of nodes synchronize more easily. The paper also presents the numerical simulations for theoretical result and shows a compromise between the theoretical and numerical results.

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Petit, Julien, Timoteo Carletti, Malbor Asllani, and Duccio Fanelli. "Delay-induced Turing-like waves for one-species reaction-diffusion model on a network." EPL (Europhysics Letters) 111, no. 5 (September 1, 2015): 58002. http://dx.doi.org/10.1209/0295-5075/111/58002.

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Hwang, Seungtaik, Jörg Kärger, and Erich Miersemann. "Diffusion and reaction in pore hierarchies by the two-region model." Adsorption 27, no. 5 (March 19, 2021): 761–76. http://dx.doi.org/10.1007/s10450-021-00307-x.

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AbstractThe two-region (“Kärger”) model of diffusion in complex pore spaces is exploited for quantitating mass transfer in hierarchically organized nanoporous materials, consisting of a continuous microporous bulk phase permeated by a network of transport pores. With the implications that the diffusivity in the transport pores significantly exceeds the diffusivity in the micropores and that the relative population of the transport pores is far below that of the micropores, overall transport depends on only three independent parameters. Depending on their interrelation, enhancement of the overall mass transfer is found to be ensured by two fundamentally different mechanisms. They are referred to as the limiting cases of fast and slow exchange, with the respective time constants of molecular uptake being controlled by different parameters. Complemented with reaction terms, the two-region model may equally successfully be applied to the quantitation of the combined effect of diffusion and reaction in terms of the effectiveness factor. Generalization of the classical Thiele concept is shown to provide an excellent estimate of the effectiveness factor of a chemical reaction in hierarchically porous materials, solely based on the intrinsic reaction rate and the time constant of molecular uptake relevant to the given conditions.

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Cantin, Guillaume, M. A. Aziz-Alaoui, and Nathalie Verdière. "Large-time dynamics in complex networks of reaction–diffusion systems applied to a panic model." IMA Journal of Applied Mathematics 84, no. 5 (September 27, 2019): 974–1000. http://dx.doi.org/10.1093/imamat/hxz022.

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Abstract This paper is devoted to the analysis of the asymptotic behaviour of a complex network of reaction–diffusion systems for a geographical model, which was proposed recently, in order to better understand behavioural reactions of individuals facing a catastrophic event. After stating sufficient conditions for the problem to admit a positively invariant region, we establish energy estimates and prove the existence of a family of exponential attractors. We explore the influence of the size of the network on the nature of those attractors, in correspondence with the geographical background. Numerical simulations illustrate our theoretical results and show the various possible dynamics of the problem.

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Chyzh, Olga V., and Mark S. Kaiser. "A Local Structure Graph Model: Modeling Formation of Network Edges as a Function of Other Edges." Political Analysis 27, no. 4 (May 6, 2019): 397–414. http://dx.doi.org/10.1017/pan.2019.8.

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Localized network processes are central to the study of political science, whether in the formation of political coalitions and voting blocs, balancing and bandwagoning, policy learning, imitation, diffusion, tipping-point dynamics, or cascade effects. These types of processes are not easily modeled using traditional network approaches, which focus on global rather than local structures within networks. We show that localized network processes, in which network edges form in response to the formation of other edges, are best modeled by shifting from the traditional theoretical framework of nodes-as-actors to what we term a nodes-as-actions framework, which allows for zeroing in on relationships among network connections. We show that the proposed theoretical framework is statistically compatible with a local structure graph model (LSGM). We demonstrate the properties of LSGMs using a Monte Carlo experiment and explore action–reaction processes in two empirical applications: formation of alliances among countries and legislative cosponsorships in the US Senate.

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Vadde, Batthula Vijaya Lakshmi, and Adrienne H. K. Roeder. "Can the French flag and reaction–diffusion models explain flower patterning? Celebrating the 50th anniversary of the French flag model." Journal of Experimental Botany 71, no. 10 (February 4, 2020): 2886–97. http://dx.doi.org/10.1093/jxb/eraa065.

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Abstract It has been 50 years since Lewis Wolpert introduced the French flag model proposing the patterning of different cell types based on threshold concentrations of a morphogen diffusing in the tissue. Sixty-seven years ago, Alan Turing introduced the idea of patterns initiating de novo from a reaction–diffusion network. Together these models have been used to explain many patterning events in animal development, so here we take a look at their applicability to flower development. First, although many plant transcription factors move through plasmodesmata from cell to cell, in the flower there is little evidence that they specify fate in a concentration-dependent manner, so they cannot yet be described as morphogens. Secondly, the reaction–diffusion model appears to be a reasonably good description of the formation of spots of pigment on petals, although additional nuances are present. Thirdly, aspects of both of these combine in a new fluctuation-based patterning system creating the scattered pattern of giant cells in Arabidopsis sepals. In the future, more precise imaging and manipulations of the dynamics of patterning networks combined with mathematical modeling will allow us to better understand how the multilayered complex and beautiful patterns of flowers emerge de novo.

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Ma, Xuerong, Shuling Shen, and Linhe Zhu. "Complex dynamic analysis of a reaction-diffusion network information propagation model with non-smooth control." Information Sciences 622 (April 2023): 1141–61. http://dx.doi.org/10.1016/j.ins.2022.12.013.

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Hollewand, M. P., and L. F. Gladden. "Modelling of diffusion and reaction in porous catalysts using a random three-dimensional network model." Chemical Engineering Science 47, no. 7 (May 1992): 1761–70. http://dx.doi.org/10.1016/0009-2509(92)85023-5.

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MATTHÄUS, FRANZISKA. "THE SPREAD OF PRION DISEASES IN THE BRAIN — MODELS OF REACTION AND TRANSPORT ON NETWORKS." Journal of Biological Systems 17, no. 04 (December 2009): 623–41. http://dx.doi.org/10.1142/s0218339009003010.

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In this paper we will present a modeling approach to describe the progression and the spread of prion diseases in the brain. Although there exist a number of mathematical models for the interaction of prions with their native counterpart, prion transport and spread is usually neglected. The concentration dynamics of prions, and thus the dynamics of the disease progression, however, are influenced by prion transport, especially in a medium as complex as the brain. Therefore, we focus here on the interaction between prion concentration dynamics and prion transport. The model is constructed by combining a model of prion-prion interaction with transport on networks. The approach leads to a system of reaction-diffusion equations, whereby the diffusion term is discrete. The equations are solved numerically on domains given as large networks. We show that the prion concentration grows faster on networks characterized by a higher degree heterogeneity. Furthermore, we introduce cell death as a consequence of increasing prion concentration, leading to network decomposition. We show that infectious diseases destroy networks similarly to targeted attacks, namely by affecting the nodes with the highest degree first. Relating the incubation period and disease progression to the process of network decomposition, we find that, interestingly, a long incubation time followed by sudden onset and fast progression of the disease does not need to be reflected in the overall concentration dynamics of the infective agent.

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Hinzpeter, Florian, Filipe Tostevin, and Ulrich Gerland. "Regulation of reaction fluxes via enzyme sequestration and co-clustering." Journal of The Royal Society Interface 16, no. 156 (July 2019): 20190444. http://dx.doi.org/10.1098/rsif.2019.0444.

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Experimental observations suggest that cells change the intracellular localization of key enzymes to regulate the reaction fluxes in enzymatic networks. In particular, cells appear to use sequestration and co-clustering of enzymes as spatial regulation strategies. These strategies should be equally useful to achieve rapid flux regulation in synthetic biomolecular systems. Here, we leverage a theoretical model to analyse the capacity of enzyme sequestration and co-clustering to control the reaction flux in a branch of a reaction–diffusion network. We find that in both cases, the response of the system is determined by two dimensionless parameters, the ratio of total activities of the competing enzymes and the ratio of diffusion to reaction timescales. Using these dependencies, we determine the parameter range for which sequestration and co-clustering can yield a biologically significant regulatory effect. Based on the known kinetic parameters of enzymes, we conclude that sequestration and co-clustering represent a viable regulation strategy for a large fraction of metabolic enzymes, and suggest design principles for reaction flux regulation in natural or synthetic systems.

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Grubišić, Luka, Marko Hajba, and Domagoj Lacmanović. "Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential." Entropy 23, no. 1 (January 11, 2021): 95. http://dx.doi.org/10.3390/e23010095.

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We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm.

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Grubišić, Luka, Marko Hajba, and Domagoj Lacmanović. "Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential." Entropy 23, no. 1 (January 11, 2021): 95. http://dx.doi.org/10.3390/e23010095.

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We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm.

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Du, Zhao, Qian Liu, and Yuxuan Yang. "The catalytic kinetics and cfd simulation of multi-stage combined removal of acrylonitrile tail gas." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 7 (2021): 115–25. http://dx.doi.org/10.17223/00213411/64/7/115.

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There is no kinetic data and rate equation that can be used directly for catalytic combustion of acrylonitrile tail gas, which leads to the multi-stage combined catalytic kinetic model of acrylonitrile tail gas collaborative removal. In the actual application process, affected by the internal and external diffusion, this paper proposes the multi-stage combined catalytic kinetic research and CFD simulation analysis of acrylonitrile tail gas collaborative removal. Based on the judgment of multi-stage combined catalytic reaction rules of acrylonitrile tail gas collaborative removal, the multi-stage combined catalytic reaction network of acrylonitrile tail gas collaborative removal is solved by matrix transformation. The possible reaction path in the multi-stage combined catalytic reaction network of acrylonitrile tail gas collaborative removal is solved. For quantitative calculation of product distribution, each step of reaction parameters and dynamic factors are required. According to the mechanism of positive carbon ion reaction, materials were used Studio software and genetic algorithm are used to calculate the dynamic factors and determine the dynamic parameters; the grid automatic generator AutoGrid5 embedded in the Fine/TurboTM software package is used to generate the CFD simulation network, and the iterative algorithm is used to calculate the limit value of the CFD simulation; the S-A model in the CFD simulation platform is used to get the modified value of the dynamic mathematical model, and the dynamic factors and parameters are brought into it to establish the CA mathematical model of multi-stage combined catalytic kinetics for the CO removal of olefine and nitrile tail gas. The experimental results show that, under the same experimental device and parameters, the internal and external diffusion effects of the multi-stage combined catalytic kinetic model of acrylonitrile tail gas collaborative removal are detected. The multi-stage combined catalytic kinetic model of acrylonitrile tail gas collaborative removal in this study uses 10-20 mesh catalyst, and the retention time of acrylonitrile tail gas is less than 4.62 s, the internal and external diffusion will not affect the acrylonitrile tail gas collaborative removal The practical application of the kinetic model for the removal of multi-stage combined catalysis.

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Nagatani, Takashi, and Genki Ichinose. "Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks." Complexity 2020 (October 9, 2020): 1–8. http://dx.doi.org/10.1155/2020/6976328.

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We present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors (R-to-S) occurs with rate μ. In the network, a node represents a patch where the RPS game is performed. RPS individuals migrate among nodes by diffusion. The dynamics are represented by the reaction-diffusion equations with the recursion formula. We study where and how species coexist or go extinct in the scale-free network. We numerically obtained the solutions for the metapopulation dynamics and derived the transition points. The results show that, with increasing mutation rate μ, the extinction of P species occurs and then the extinction of R species occurs, and finally only S species survives. Thus, the first and second dynamical phase transitions occur in the scale-free hierarchical network. We also show that the scaling law holds for the population dynamics which suggests that the transition points approach zero in the limit of infinite size.

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Umeno, Yoshitaka, Emi Kawai, Atsushi Kubo, Hiroyuki Shima, and Takashi Sumigawa. "Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network." Materials 16, no. 5 (March 5, 2023): 2108. http://dx.doi.org/10.3390/ma16052108.

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The reaction–diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction–diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls (p2), and the average width of the walls (p3). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in p2 and p3 for test data having 10% deviation from the training data were within 7% of the average magnitude of p2 and p3. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework.

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Crevat, Joachim. "Asymptotic limit of a spatially-extended mean-field FitzHugh–Nagumo model." Mathematical Models and Methods in Applied Sciences 30, no. 05 (May 2020): 957–90. http://dx.doi.org/10.1142/s0218202520500207.

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We consider a spatially extended mean-field model of a FitzHugh–Nagumo neural network, with a rescaled interaction kernel. Our main purpose is to prove that its asymptotic limit in the regime of strong local interactions converges toward a system of reaction–diffusion equations taking account for the average quantities of the network. Our approach is based on a modulated energy argument, to compare the macroscopic quantities computed from the solution of the transport equation, and the solution of the limit system. The main difficulty, compared to the literature, lies in the need of regularity in space of the solutions of the limit system and a careful control of an internal nonlocal dissipation.

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Chang, Lili, Luyao Guo, Chen Liu, Zhen Wang, and Guiquan Sun. "The qualitative and quantitative relationships between pattern formation and average degree in networked reaction-diffusion systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 9 (September 2022): 093129. http://dx.doi.org/10.1063/5.0107504.

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The Turing pattern is an important dynamic behavior characteristic of activator–inhibitor systems. Differentiating from traditional assumption of activator–inhibitor interactions in a spatially continuous domain, a Turing pattern in networked reaction-diffusion systems has received much attention during the past few decades. In spite of its great progress, it still fails to evaluate the precise influences of network topology on pattern formation. To this end, we try to promote the research on this important and interesting issue from the point of view of average degree—a critical topological feature of networks. We first qualitatively analyze the influence of average degree on pattern formation. Then, a quantitative relationship between pattern formation and average degree, the exponential decay of pattern formation, is proposed via nonlinear regression. The finding holds true for several activator–inhibitor systems including biology model, ecology model, and chemistry model. The significance of this study lies that the exponential decay not only quantitatively depicts the influence of average degree on pattern formation, but also provides the possibility for predicting and controlling pattern formation.

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Recho, Pierre, Adrien Hallou, and Edouard Hannezo. "Theory of mechanochemical patterning in biphasic biological tissues." Proceedings of the National Academy of Sciences 116, no. 12 (February 28, 2019): 5344–49. http://dx.doi.org/10.1073/pnas.1813255116.

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The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics with morphogen turnover and transport to explore routes to patterning. Our active description couples morphogen reaction and diffusion, which impact cell differentiation and tissue mechanics, to a two-phase poroelastic rheology, where one tissue phase consists of a poroelastic cell network and the other one of a permeating extracellular fluid, which provides a feedback by actively transporting morphogens. While this model encompasses previous theories approximating tissues to inert monophasic media, such as Turing’s reaction–diffusion model, it overcomes some of their key limitations permitting pattern formation via any two-species biochemical kinetics due to mechanically induced cross-diffusion flows. Moreover, we describe a qualitatively different advection-driven Keller–Segel instability which allows for the formation of patterns with a single morphogen and whose fundamental mode pattern robustly scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.

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Lin, Shanrong, Yanli Huang, and Erfu Yang. "Passivity and Synchronization of Coupled Different Dimensional Delayed Reaction-Diffusion Neural Networks with Dirichlet Boundary Conditions." Complexity 2020 (January 8, 2020): 1–21. http://dx.doi.org/10.1155/2020/4987962.

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Two types of coupled different dimensional delayed reaction-diffusion neural network (CDDDRDNN) models without and with parametric uncertainties are analyzed in this paper. On the one hand, passivity and synchronization of the raised network model with certain parameters are studied through exploiting some inequality techniques and Lyapunov stability theory, and some adequate conditions are established. On the other hand, the problems of robust passivity and robust synchronization of CDDDRDNNs with parameter uncertainties are solved. Finally, two numerical examples are given to testify the effectiveness of the derived passivity and synchronization conditions.

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Tyagi, Swati, Subit K. Jain, Syed Abbas, Shahlar Meherrem, and Rajendra K. Ray. "Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term." Neurocomputing 313 (November 2018): 306–15. http://dx.doi.org/10.1016/j.neucom.2018.06.008.

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Goode, P. "Seismic Solar Model." Highlights of Astronomy 10 (1995): 326–27. http://dx.doi.org/10.1017/s1539299600011370.

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The method of frequency inversion reveals that within the quoted observational errors, it is possible to achieve a precision of ∼ 10−3 in the sound speed determination through most of the Sun’s interior. Only for r < 0.05R⊙ is the precision ∼ 10−2. The accuracy of the density and pressure determinations is only slightly worse. Such restrictions impose significant constraints on the microscopic physical data, i.e. opacities, nuclear reaction cross-sections, and diffusion coefficients as well as on the solar age. The helioseismic age is consistent with that from meteorites.Recently released low-l solar oscillation data from the BISON network combined with BBSO data yield the most up-to-date solar seismic model of the Sun’s interior. For the core, the solar seismic model from the new data are consistent with the best, current standard solar models. An astrophysical solution to the solar neutrino problem fades away.

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Rolison, Debra R. "(Keynote) Integrating Catalytic and Transport Functions within Multiscale Architectures." ECS Meeting Abstracts MA2018-01, no. 31 (April 13, 2018): 1843. http://dx.doi.org/10.1149/ma2018-01/31/1843.

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Our team at the U.S. Naval Research Laboratory is pursuing an opportunity unique within heterogeneous catalytic science: Correlating catalytic activity to our ability to integrate multiple transport and reactivity functions within practical, not model, architectures. We exploit sol–gel-derived aerogels as a hierarchical platform—structurally complex, but functionally simple—to address in detail whether controlling ionic transport to three-phase boundaries affects the catalytic activity of AuNP–modified oxide nanoarchitectures for model, CO-centered reactions and for the oxidation of water and alcohols. We can also address whether long ionic diffusion lengths (determined via impedance measurements) correlate with local ion mobility near the catalysis zone (monitored by NMR spectroscopy) and does either length scale affect catalytic activity (tracked by determining reaction turnover frequency)? Our synthetic processing protocols to control pore–solid architectures are established, ranging from a continuous 3D porous network with 1–100 nm pores (aerogel) to a continuous 3D porous network containing only 10–50 nm mesopores (ambigel) to a collapsed porous network with 10 nm pores (xerogel). The choice of architecture determines the through-connectedness of two critical transport networks: electrical wiring along the solid network and facile molecular flux through the pore network (approaching open-medium diffusion rates). This class of hierarchical nanoarchitectures provides a tunable platform with which to develop comprehensive mechanistic understanding that will allow us to design next-generation catalytic architectures with superior performance.

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Payton, Ryan L., Yizhuo Sun, Domenico Chiarella, and Andrew Kingdon. "Pore Scale Numerical Modelling of Geological Carbon Storage Through Mineral Trapping Using True Pore Geometries." Transport in Porous Media 141, no. 3 (January 10, 2022): 667–93. http://dx.doi.org/10.1007/s11242-021-01741-9.

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Abstract Mineral trapping (MT)is the most secure method of sequestering carbon for geologically significant periods of time. The processes behind MT fundamentally occur at the pore scale, therefore understanding which factors control MT at this scale is crucial. We present a finite elements advection–diffusion–reaction numerical model which uses true pore geometry model domains generated from $$\upmu$$ μ CT imaging. Using this model, we investigate the impact of pore geometry features such as branching, tortuosity and throat radii on the distribution and occurrence of carbonate precipitation in different pore networks over 2000 year simulated periods. We find evidence that a greater tortuosity, greater degree of branching of a pore network and narrower pore throats are detrimental to MT and contribute to the risk of clogging and reduction of connected porosity. We suggest that a tortuosity of less than 2 is critical in promoting greater precipitation per unit volume and should be considered alongside porosity and permeability when assessing reservoirs for geological carbon storage (GCS). We also show that the dominant influence on precipitated mass is the Damköhler number, or reaction rate, rather than the availability of reactive minerals, suggesting that this should be the focus when engineering effective subsurface carbon storage reservoirs for long term security. Article Highlights The rate of reaction has a stronger influence on mineral precipitation than the amount of available reactant. In a fully connected pore network preferential flow pathways still form which results in uneven precipitate distribution. A pore network tortuosity of <2 is recommended to facilitate greater carbon mineralisation.

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Khan, Naveed Ahmad, Fahad Sameer Alshammari, Carlos Andrés Tavera Romero, Muhammad Sulaiman, and Ghaylen Laouini. "Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor." Molecules 26, no. 23 (December 2, 2021): 7310. http://dx.doi.org/10.3390/molecules26237310.

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In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.

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COCHO, G., A. GELOVER-SANTIAGO, G. MARTINEZ-MEKLER, and A. RODIN. "NONLINEAR MODELING OF THE AIDS VIRUS GENETIC SEQUENCE EVOLUTION." International Journal of Modern Physics C 05, no. 02 (April 1994): 321–24. http://dx.doi.org/10.1142/s0129183194000404.

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A network of coupled maps is introduced to model the evolution of the genetic sequence of the HIV1 AIDS virus. Within a space of RNA chemical composition, short range interactions correspond to mutations. Ecological constraints generate long range couplings. The resulting equations are of a reaction-diffusion type. Quasi-species with an error threshold emerge from the model dynamics. Predictions relating chemical composition regularity properties with the variability of the HIV RNA sequence agree with a statistical analysis from gene data banks. The model suggests a clue for an alternative therapeutical treatment.

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Journal articles on the topic 'Reaction-Diffusion Network Model'

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