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Статті в журналах з теми "Cross-population diffusion"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Chen, Li, and Ansgar Jüngel. "Analysis of a parabolic cross-diffusion population model without self-diffusion." Journal of Differential Equations 224, no. 1 (May 2006): 39–59. http://dx.doi.org/10.1016/j.jde.2005.08.002.

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2

Galiano, Gonzalo, and Julián Velasco. "Well-Posedness of a Cross-Diffusion Population Model with Nonlocal Diffusion." SIAM Journal on Mathematical Analysis 51, no. 4 (January 2019): 2884–902. http://dx.doi.org/10.1137/18m1229249.

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3

van Everdingen, Yvonne M., Wouter B. Aghina, and Dennis Fok. "Forecasting cross-population innovation diffusion: A Bayesian approach." International Journal of Research in Marketing 22, no. 3 (September 2005): 293–308. http://dx.doi.org/10.1016/j.ijresmar.2004.11.003.

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4

Yamada, Yoshio, and Kousuke Kuto. "On limit systems for some population models with cross-diffusion." Discrete and Continuous Dynamical Systems - Series B 17, no. 8 (July 2012): 2745–69. http://dx.doi.org/10.3934/dcdsb.2012.17.2745.

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5

Dhariwal, Gaurav, Ansgar Jüngel, and Nicola Zamponi. "Global martingale solutions for a stochastic population cross-diffusion system." Stochastic Processes and their Applications 129, no. 10 (October 2019): 3792–820. http://dx.doi.org/10.1016/j.spa.2018.11.001.

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6

Zamponi, Nicola, and Ansgar Jüngel. "Analysis of degenerate cross-diffusion population models with volume filling." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 34, no. 1 (January 2017): 1–29. http://dx.doi.org/10.1016/j.anihpc.2015.08.003.

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7

Barrett, John W., and James F. Blowey. "Finite element approximation of a nonlinear cross-diffusion population model." Numerische Mathematik 98, no. 2 (June 15, 2004): 195–221. http://dx.doi.org/10.1007/s00211-004-0540-y.

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8

Le, Dung. "Global Existence for some Cross Diffusion Systems with Equal Cross Diffusion/Reaction Rates." Advanced Nonlinear Studies 20, no. 4 (November 1, 2020): 833–45. http://dx.doi.org/10.1515/ans-2020-2096.

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Анотація:

AbstractWe consider some cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada–Kawasaki–Teramoto (SKT) model in population biology. We establish the global existence of strong solutions to systems for multiple species having equal either diffusion or reaction rates. The systems are given on bounded domains of arbitrary dimension.

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9

Wang, Weiming, Zhengguang Guo, R. K. Upadhyay, and Yezhi Lin. "Pattern Formation in a Cross-Diffusive Holling-Tanner Model." Discrete Dynamics in Nature and Society 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/828219.

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Анотація:

We present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; Hopf and Turing bifurcation in a spatial domain is presented, too. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to spots, but also to strips, holes, and stripes-spots replication. And the methods and results in the present paper may be useful for the research of the pattern formation in the cross-diffusive model.

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10

CAPASSO, V., A. DI LIDDO, F. NOTARNICOLA, and L. RUSSO. "EPIDEMIC REACTION-DIFFUSION SYSTEM WITH CROSS-DIFFUSION: MODELING AND NUMERICAL SOLUTION." Journal of Biological Systems 03, no. 03 (September 1995): 733–46. http://dx.doi.org/10.1142/s0218339095000678.

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Анотація:

Reaction-diffusion systems with cross-diffusion are analyzed here for modeling the population dynamics of epidemic systems. In this paper specific attention is devoted to the numerical analysis and simulation of such systems to show that, far from possible pathologies, the qualitative behaviour of the systems may well interpret the dynamics of real systems.

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11

Chen, Li, and Ansgar Jüngel. "Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion." SIAM Journal on Mathematical Analysis 36, no. 1 (January 2004): 301–22. http://dx.doi.org/10.1137/s0036141003427798.

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12

Galiano, Gonzalo, and Virginia Selgas. "Analysis of a splitting–differentiation population model leading to cross-diffusion." Computers & Mathematics with Applications 70, no. 12 (December 2015): 2933–45. http://dx.doi.org/10.1016/j.camwa.2015.10.005.

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13

Jüngel, Ansgar, and Nicola Zamponi. "Qualitative behavior of solutions to cross-diffusion systems from population dynamics." Journal of Mathematical Analysis and Applications 440, no. 2 (August 2016): 794–809. http://dx.doi.org/10.1016/j.jmaa.2016.03.076.

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14

Chen, Xiuqing, Esther S. Daus, and Ansgar Jüngel. "Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species." Archive for Rational Mechanics and Analysis 227, no. 2 (September 15, 2017): 715–47. http://dx.doi.org/10.1007/s00205-017-1172-6.

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15

Shao, Yangyang, Yan Meng, and Xinyue Xu. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect." Mathematics 10, no. 9 (May 1, 2022): 1500. http://dx.doi.org/10.3390/math10091500.

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Анотація:

The Allee effect is widespread among endangered plants and animals in ecosystems, suggesting that a minimum population density or size is necessary for population survival. This paper investigates the stability and pattern formation of a predator–prey model with nonlinear reactive cross-diffusion under Neumann boundary conditions, which introduces the Allee effect. Firstly, the ODE system is asymptotically stable for its positive equilibrium solution. In a reaction system with self-diffusion, the Allee effect can destabilize the system. Then, in a reaction system with cross-diffusion, through a linear stability analysis, the cross-diffusion coefficient is used as a bifurcation parameter, and instability conditions driven by the cross-diffusion are obtained. Furthermore, we show that the system (5) has at least one inhomogeneous stationary solution. Finally, our theoretical results are illustrated with numerical simulations.

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16

Zhang, Guohong, and Xiaoli Wang. "Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/167856.

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Анотація:

We study a Lotka-Volterra type predator-prey model with a transmissible disease in the predator population. We concentrate on the effect of diffusion and cross-diffusion on the emergence of stationary patterns. We first show that both self-diffusion and cross-diffusion can not cause Turing instability from the disease-free equilibria. Then we find that the endemic equilibrium remains linearly stable for the reaction diffusion system without cross-diffusion, while it becomes linearly unstable when cross-diffusion also plays a role in the reaction-diffusion system; hence, the instability is driven solely from the effect of cross-diffusion. Furthermore, we derive some results for the existence and nonexistence of nonconstant stationary solutions when the diffusion rate of a certain species is small or large.

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17

Wang, Xiaoqin, and Yongli Cai. "Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/306467.

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Анотація:

We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.

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18

LI, AN-WEI, ZHEN JIN, LI LI, and JIAN-ZHONG WANG. "EMERGENCE OF OSCILLATORY TURING PATTERNS INDUCED BY CROSS DIFFUSION IN A PREDATOR–PREY SYSTEM." International Journal of Modern Physics B 26, no. 31 (December 4, 2012): 1250193. http://dx.doi.org/10.1142/s0217979212501937.

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Анотація:

In this paper, we presented a predator–prey model with self diffusion as well as cross diffusion. By using theory on linear stability, we obtain the conditions on Turing instability. The results of numerical simulations reveal that oscillating Turing patterns with hexagons arise in the system. And the values of the parameters we choose for simulations are outside of the Turing domain of the no cross diffusion system. Moreover, we show that cross diffusion has an effect on the persistence of the population, i.e., it causes the population to run a risk of extinction. Particularly, our results show that, without interaction with either a Hopf or a wave instability, the Turing instability together with cross diffusion in a predator–prey model can give rise to spatiotemporally oscillating solutions, which well enrich the finding of pattern formation in ecology.

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19

ANDREIANOV, BORIS, MOSTAFA BENDAHMANE, and RICARDO RUIZ-BAIER. "ANALYSIS OF A FINITE VOLUME METHOD FOR A CROSS-DIFFUSION MODEL IN POPULATION DYNAMICS." Mathematical Models and Methods in Applied Sciences 21, no. 02 (February 2011): 307–44. http://dx.doi.org/10.1142/s0218202511005064.

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Анотація:

The main goal of this paper is to propose a convergent finite volume method for a reaction–diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a spacetime L1 compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

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20

Ouedraogo, Hamidou, Wendkouni Ouedraogo, and Boureima Sangare. "Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion." BIOMATH 8, no. 2 (December 16, 2019): 1911237. http://dx.doi.org/10.11145/j.biomath.2019.11.237.

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Анотація:

In this paper we propose a nonlinear reaction-diffusion system describing the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibria based on some conditions on self- and cross-diffusion coefficients. The analytical findings are verified by numerical simulation.

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21

Kennedy, T. A. B., and S. Swain. "Population trapping with cross-correlated lasers of non-Lorentzian (phase diffusion) bandshape." Journal of Physics B: Atomic and Molecular Physics 18, no. 23 (December 14, 1985): 4639–46. http://dx.doi.org/10.1088/0022-3700/18/23/015.

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22

Kennedy, T. A. B., and S. Swain. "Population trapping with cross-correlated lasers of non-Lorentzian (phase diffusion) bandshape." Journal of Physics B: Atomic and Molecular Physics 19, no. 16 (August 28, 1986): 2599. http://dx.doi.org/10.1088/0022-3700/19/16/519.

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23

Dreher, Michael. "Analysis of a population model with strong cross-diffusion in unbounded domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 138, no. 04 (July 28, 2008): 769–86. http://dx.doi.org/10.1017/s0308210506001259.

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24

Francesca Carfora, Maria, and Isabella Torcicollo. "Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense." Mathematics 8, no. 8 (July 30, 2020): 1244. http://dx.doi.org/10.3390/math8081244.

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Анотація:

In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.

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25

Wang, Pengfei, Min Zhao, Hengguo Yu, Chuanjun Dai, Nan Wang, and Beibei Wang. "Nonlinear Dynamics of a Toxin-Phytoplankton-Zooplankton System with Self- and Cross-Diffusion." Discrete Dynamics in Nature and Society 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4893451.

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Анотація:

A nonlinear system describing the interaction between toxin-producing phytoplankton and zooplankton was investigated analytically and numerically, where the system was represented by a couple of reaction-diffusion equations. We analyzed the effect of self- and cross-diffusion on the system. Some conditions for the local and global stability of the equilibrium were obtained based on the theoretical analysis. Furthermore, we found that the equilibrium lost its stability via Turing instability and patterns formation then occurred. In particular, the analysis indicated that cross-diffusion can play an important role in pattern formation. Subsequently, we performed a series of numerical simulations to further study the dynamics of the system, which demonstrated the rich dynamics induced by diffusion in the system. In addition, the numerical simulations indicated that the direction of cross-diffusion can influence the spatial distribution of the population and the population density. The numerical results agreed with the theoretical analysis. We hope that these results will prove useful in the study of toxic plankton systems.

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26

LI, HUICONG, RUI PENG, and TIAN XIANG. "Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion." European Journal of Applied Mathematics 31, no. 1 (September 18, 2018): 26–56. http://dx.doi.org/10.1017/s0956792518000463.

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Анотація:

This paper is concerned with two frequency-dependent susceptible–infected–susceptible epidemic reaction–diffusion models in heterogeneous environment, with a cross-diffusion term modelling the effect that susceptible individuals tend to move away from higher concentration of infected individuals. It is first shown that the corresponding Neumann initial-boundary value problem in an n-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly in-time bounded regardless of the strength of the cross-diffusion and the spatial dimension n. It is further shown that, even in the presence of cross-diffusion, the models still admit threshold-type dynamics in terms of the basic reproduction number $\mathcal {R}_0$ – i.e. the unique disease-free equilibrium is globally stable if $\mathcal {R}_0\lt1$, while if $\mathcal {R}_0\gt1$, the disease is uniformly persistent and there is an endemic equilibrium (EE), which is globally stable in some special cases with weak chemotactic sensitivity. Our results on the asymptotic profiles of EE illustrate that restricting the motility of susceptible population may eliminate the infectious disease entirely for the first model with constant total population but fails for the second model with varying total population. In particular, this implies that such cross-diffusion does not contribute to the elimination of the infectious disease modelled by the second one.

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27

Tao, Youshan, and Michael Winkler. "Boundedness and stabilization in a population model with cross‐diffusion for one species." Proceedings of the London Mathematical Society 119, no. 6 (July 25, 2019): 1598–632. http://dx.doi.org/10.1112/plms.12276.

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28

Kondratyev, Stanislav, Léonard Monsaingeon, and Dmitry Vorotnikov. "A fitness-driven cross-diffusion system from population dynamics as a gradient flow." Journal of Differential Equations 261, no. 5 (September 2016): 2784–808. http://dx.doi.org/10.1016/j.jde.2016.05.012.

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29

Wen, Zijuan, and Shengmao Fu. "Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics." Journal of Computational and Applied Mathematics 230, no. 1 (August 2009): 34–43. http://dx.doi.org/10.1016/j.cam.2008.10.064.

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30

SUN, GUI-QUAN, ZHEN JIN, YI-GUO ZHAO, QUAN-XING LIU, and LI LI. "SPATIAL PATTERN IN A PREDATOR-PREY SYSTEM WITH BOTH SELF- AND CROSS-DIFFUSION." International Journal of Modern Physics C 20, no. 01 (January 2009): 71–84. http://dx.doi.org/10.1142/s0129183109013467.

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Анотація:

The vast majority of models for spatial dynamics of natural populations assume a homogeneous physical environment. However, in practice, dispersing organisms may encounter landscape features that significantly inhibit their movement. And spatial patterns are ubiquitous in nature, which can modify the temporal dynamics and stability properties of population densities at a range of spatial scales. Thus, in this paper, a predator-prey system with Michaelis-Menten-type functional response and self- and cross-diffusion is investigated. Based on the mathematical analysis, we obtain the condition of the emergence of spatial patterns through diffusion instability, i.e., Turing pattern. A series of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe-like or spotted or coexistence of both. The obtained results show that the interaction of self-diffusion and cross-diffusion plays an important role on the pattern formation of the predator-prey system.

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31

Kumari, Nitu, and Nishith Mohan. "Cross Diffusion Induced Turing Patterns in a Tritrophic Food Chain Model with Crowley-Martin Functional Response." Mathematics 7, no. 3 (March 1, 2019): 229. http://dx.doi.org/10.3390/math7030229.

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Анотація:

Diffusion has long been known to induce pattern formation in predator prey systems. For certain prey-predator interaction systems, self diffusion conditions ceases to induce patterns, i.e., a non-constant positive solution does not exist, as seen from the literature. We investigate the effect of cross diffusion on the pattern formation in a tritrophic food chain model. In the formulated model, the prey interacts with the mid level predator in accordance with Holling Type II functional response and the mid and top level predator interact via Crowley-Martin functional response. We prove that the stationary uniform solution of the system is stable in the presence of diffusion when cross diffusion is absent. However, this solution is unstable in the presence of both self diffusion and cross diffusion. Using a priori analysis, we show the existence of a inhomogeneous steady state. We prove that no non-constant positive solution exists in the presence of diffusion under certain conditions, i.e., no pattern formation occurs. However, pattern formation is induced by cross diffusion because of the existence of non-constant positive solution, which is proven analytically as well as numerically. We performed extensive numerical simulations to understand Turing pattern formation for different values of self and cross diffusivity coefficients of the top level predator to validate our results. We obtained a wide range of Turing patterns induced by cross diffusion in the top population, including floral, labyrinth, hot spots, pentagonal and hexagonal Turing patterns.

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32

Galiano, Gonzalo. "On a cross-diffusion population model deduced from mutation and splitting of a single species." Computers & Mathematics with Applications 64, no. 6 (September 2012): 1927–36. http://dx.doi.org/10.1016/j.camwa.2012.03.045.

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33

UPADHYAY, RANJIT KUMAR, ATASI PATRA, B. DUBEY, and N. K. THAKUR. "A PREDATOR–PREY INTERACTION MODEL WITH SELF- AND CROSS-DIFFUSION IN AQUATIC SYSTEMS." Journal of Biological Systems 22, no. 04 (November 11, 2014): 691–712. http://dx.doi.org/10.1142/s0218339014500284.

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Анотація:

In this paper, the complex dynamics of a spatial aquatic system in the presence of self- and cross-diffusion are investigated. Criteria for local stability, instability and global stability are obtained. The effect of critical wavelength which can drive a system to instability is investigated. We noticed that cross-diffusion coefficient can be quite significant, even for small values of off-diagonal terms in the diffusion matrix. With the help of numerical simulation, we observed the Turing patterns (spots, strips, spot-strips mixture), regular spiral patterns and irregular patchy structures. The beauty and complexity of the Turing patterns are attributed to a large variety of symmetry properties realized by different values of predator's immunity, rate of fish predation and half saturation constant of predator population.

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34

Galiano, Gonzalo, and Julián Velasco. "Competing through altering the environment: A cross-diffusion population model coupled to transport–Darcy flow equations." Nonlinear Analysis: Real World Applications 12, no. 5 (October 2011): 2826–38. http://dx.doi.org/10.1016/j.nonrwa.2011.04.009.

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35

Liu, Yuanyuan, and Youshan Tao. "Dynamics in a parabolic–elliptic two-species population competition model with cross-diffusion for one species." Journal of Mathematical Analysis and Applications 456, no. 1 (December 2017): 1–15. http://dx.doi.org/10.1016/j.jmaa.2017.05.058.

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36

Galiano, Gonzalo, Mar�a L. Garz�n, and Ansgar J�ngel. "Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model." Numerische Mathematik 93, no. 4 (February 1, 2003): 655–73. http://dx.doi.org/10.1007/s002110200406.

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37

Chen, Xiuqing, and Ansgar Jüngel. "Weak–strong uniqueness of renormalized solutions to reaction–cross-diffusion systems." Mathematical Models and Methods in Applied Sciences 29, no. 02 (February 2019): 237–70. http://dx.doi.org/10.1142/s0218202519500088.

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Анотація:

The weak–strong uniqueness for renormalized solutions to reaction–cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada–Kawasaki–Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based on the evolution of the relative entropy modified by suitable cutoff functions.

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38

Mori, Tatsuki, Takashi Suzuki, and Shoji Yotsutani. "Numerical approach to existence and stability of stationary solutions to a SKT cross-diffusion equation." Mathematical Models and Methods in Applied Sciences 28, no. 11 (October 2018): 2191–210. http://dx.doi.org/10.1142/s0218202518400122.

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Анотація:

The SKT cross-diffusion equation is proposed by N. Shigesada, K. Kawasaki and E. Teramoto in 1979 to investigate segregation phenomena of two competing species with each other in the same habitat area. The effect of cross-diffusion affects the population pressure between two different species. Lou and Ni derived limiting systems to see whether this effect may give rise to a spatial segregation or not, and to clarify its mechanism. In this paper, we introduce some new representation of solutions to a stationary limiting problem modified from representation by Lou, Ni and Yotsutani. We apply it to the numerical investigation of existence, non-existence, multiplicity and stability.

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39

Kaufman, Jason, and Orlando Patterson. "Cross-National Cultural Diffusion: The Global Spread of Cricket." American Sociological Review 70, no. 1 (February 2005): 82–110. http://dx.doi.org/10.1177/000312240507000105.

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This article explores the dynamics of cross-national cultural diffusion through the study of a case in which a symbolically powerful cultural practice, the traditionally English sport of cricket, successfully diffused to most but not all countries with close cultural ties to England. Neither network ties, nor national values, nor climatic conditions account for this disparity. Our explanation hinges instead on two key factors: first, the degree to which elites chose either to appropriate the game and deter others from participating or actively to promote it throughout the population for hegemonic purposes; and second, the degree to which the game was “popularized” by cultural entrepreneurs looking to get and keep spectators and athletes interested in the sport. Both outcomes relate to the nature of status hierarchies in these different societies, as well as the agency of elites and entrepreneurs in shaping the cultural valence of the game. The theoretical significance of this project is thus the observation that the diffusion of cultural practices can be promoted or discouraged by intermediaries with the power to shape the cultural meaning and institutional accessibility of such practices.

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Wang, Caiyun, Yongyong Pei, Yaqun Niu, and Ruiqiang He. "Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion." Complexity 2022 (January 10, 2022): 1–14. http://dx.doi.org/10.1155/2022/8238384.

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Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology.

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Gorchov, David L., Steven M. Castellano, and Douglas A. Noe. "Long-Distance Dispersal and Diffusion in the Invasion of Lonicera maackii." Invasive Plant Science and Management 7, no. 3 (September 2014): 464–72. http://dx.doi.org/10.1614/ipsm-d-13-00105.1.

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AbstractTo investigate the relative importance of long-distance dispersal vs. diffusion in the invasion of a nonnative plant, we used age structure to infer the contribution to recruitment of external propagule rain vs. within-population reproduction. We quantified the age structure of 14 populations of Amur honeysuckle in a landscape where it recently invaded, in Darke County, OH. We sampled the largest honeysuckle individuals in each population (woodlots), and aged these by counting annual rings in stem cross sections. Individuals in the oldest four 1-yr age classes are assumed to be from external recruitment, given the minimum age at which shrubs reproduce. We used these recruitment rates to model external recruitment over the next 5 yr and used observed age structures to estimate total recruitment. We used the difference between total and external recruitment to infer the rate of internal recruitment. Our findings indicate that recruitment from within the population is of about the same magnitude as immigration in the fifth to seventh year after population establishment, but by years 8 to 9 internal recruitment dominates. At the landscape scale, the temporal-spatial pattern of population establishment supports a stratified dispersal model, with the earliest populations establishing in widely spaced woodlots, about 4 km from existing populations, and these serving as “nascent foci” for diffusion to nearby woodlots. Understanding the relative importance of long-distance dispersal vs. diffusion will inform management, e.g., whether it is more effective to scout for isolated shrubs or remove reproducing shrubs at the edge of invaded areas.

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Van den Hof, Malon, Anne Marleen ter Haar, Matthan W. A. Caan, Rene Spijker, Johanna H. van der Lee, and Dasja Pajkrt. "Brain structure of perinatally HIV-infected patients on long-term treatment." Neurology: Clinical Practice 9, no. 5 (April 25, 2019): 433–42. http://dx.doi.org/10.1212/cpj.0000000000000637.

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ObjectiveWe aim to give an overview of the available evidence on brain structure and function in PHIV-infected patients (PHIV+) using long-term combination antiretroviral therapy (cART) and how differences change over time.MethodsWe conducted an electronic search using MEDLINE, Embase, and PsycINFO. We used the following selection criteria: cohort and cross-sectional studies that reported on brain imaging differences between PHIV+ of all ages who used cART for at least six months before neuroimaging and HIV-negative controls. Two reviewers independently selected studies, performed data extraction, and assessed quality of studies.ResultsAfter screening 1500 abstracts and 343 full-text articles, we identified 19 eligible articles. All included studies had a cross-sectional design and used MRI with different modalities: structural MRI (n = 7), diffusion tensor imaging (DTI) (n = 6), magnetic resonance spectroscopy (n = 5), arterial spin labeling (n = 1), and resting-state functional neuroimaging (n = 1). Studies showed considerable methodological limitations and heterogeneity, preventing us to perform meta-analyses. DTI data on white matter microstructure suggested poorer directional diffusion in cART-treated PHIV+ compared with controls. Other modalities were inconclusive.ConclusionEvidence may suggest brain structure and function differences in the population of PHIV+ on long-term cART compared with the HIV-negative population. Because of a small study population, and considerable heterogeneity and methodological limitations, the extent of brain structure and function differences on neuroimaging between groups remains unknown.

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Horstmann, Dirk. "On some cross-diffusion models in population dynamics and their connections to well-posed filters in signal enhancement processes." IMA Journal of Applied Mathematics 70, no. 3 (June 1, 2005): 386–99. http://dx.doi.org/10.1093/imamat/hxh036.

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Arif, Muhammad Shoaib, Kamaleldin Abodayeh, and Asad Ejaz. "On the stability of the diffusive and non-diffusive predator-prey system with consuming resources and disease in prey species." Mathematical Biosciences and Engineering 20, no. 3 (2023): 5066–93. http://dx.doi.org/10.3934/mbe.2023235.

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<abstract> <p>This research deals with formulating a multi-species eco-epidemiological mathematical model when the interacting species compete for the same food sources and the prey species have some infection. It is assumed that infection does not spread vertically. Infectious diseases severely affect the population dynamics of prey and predator. One of the most important factors in population dynamics is the movement of species in the habitat in search of resources or protection. The ecological influences of diffusion on the population density of both species are studied. The study also deals with the analysis of the effects of diffusion on the fixed points of the proposed model. The fixed points of the model are sorted out. The Lyapunov function is constructed for the proposed model. The fixed points of the proposed model are analyzed through the use of the Lyapunov stability criterion. It is proved that coexisting fixed points remain stable under the effects of self-diffusion, whereas, in the case of cross-diffusion, Turing instability exists conditionally. Moreover, a two-stage explicit numerical scheme is constructed, and the stability of the said scheme is found by using von Neumann stability analysis. Simulations are performed by using the constructed scheme to discuss the model's phase portraits and time-series solution. Many scenarios are discussed to display the present study's significance. The impacts of the transmission parameter 𝛾 and food resource <italic>f</italic> on the population density of species are presented in plots. It is verified that the availability of common food resources greatly influences the dynamics of such models. It is shown that all three classes, i.e., the predator, susceptible prey and infected prey, can coexist in the habitat, and this coexistence has a stable nature. Hence, in the realistic scenarios of predator-prey ecology, the results of the study show the importance of food availability for the interacting species.</p> </abstract>

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Zamponi, Nicola, and Ansgar Jüngel. "Corrigendum to “Analysis of degenerate cross-diffusion population models with volume filling” [Ann. Inst. Henri Poincaré 34 (1) (2017) 1–29]." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 34, no. 3 (May 2017): 789–92. http://dx.doi.org/10.1016/j.anihpc.2016.06.001.

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Fayard, Patrick, and Timothy R. Field. "Discrete Models for Scattering Populations." Journal of Applied Probability 48, no. 1 (March 2011): 285–92. http://dx.doi.org/10.1239/jap/1300198150.

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Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.

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Fayard, Patrick, and Timothy R. Field. "Discrete Models for Scattering Populations." Journal of Applied Probability 48, no. 01 (March 2011): 285–92. http://dx.doi.org/10.1017/s0021900200007774.

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Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.

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Cremer, Jonas, Igor Segota, Chih-yu Yang, Markus Arnoldini, John T. Sauls, Zhongge Zhang, Edgar Gutierrez, Alex Groisman, and Terence Hwa. "Effect of flow and peristaltic mixing on bacterial growth in a gut-like channel." Proceedings of the National Academy of Sciences 113, no. 41 (September 28, 2016): 11414–19. http://dx.doi.org/10.1073/pnas.1601306113.

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The ecology of microbes in the gut has been shown to play important roles in the health of the host. To better understand microbial growth and population dynamics in the proximal colon, the primary region of bacterial growth in the gut, we built and applied a fluidic channel that we call the “minigut.” This is a channel with an array of membrane valves along its length, which allows mimicking active contractions of the colonic wall. Repeated contraction is shown to be crucial in maintaining a steady-state bacterial population in the device despite strong flow along the channel that would otherwise cause bacterial washout. Depending on the flow rate and the frequency of contractions, the bacterial density profile exhibits varying spatial dependencies. For a synthetic cross-feeding community, the species abundance ratio is also strongly affected by mixing and flow along the length of the device. Complex mixing dynamics due to contractions is described well by an effective diffusion term. Bacterial dynamics is captured by a simple reaction–diffusion model without adjustable parameters. Our results suggest that flow and mixing play a major role in shaping the microbiota of the colon.

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Rocheleau, Jonathan V., and Nils O. Petersen. "Sendai Virus Binds to a Dispersed Population of NBD-GD1a." Bioscience Reports 20, no. 3 (June 1, 2000): 139–55. http://dx.doi.org/10.1023/a:1005559317975.

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Receptor aggregation is believed to be an important step in the attachmentof membrane enveloped virus' to target cell membranes. A likely receptorfor Sendai virus is the ganglioside GD1a. In this work we have studied themembrane diffusion of the fluorescent ganglioside NBD-GD1a on the surfaceof CV-1 cells with standard photobleaching techniques. Using confocallaser scanning microscopy (CLSM) and Image Correlation Spectroscopy(ICS) NBD-GD1a is shown to exist in at least two populations: dispersedand aggregated. By quantifying the distribution of NBD-GD1a pre- andpost-incubation with Sendai virus it is shown that the virus inducesa dose-dependent clustering of NBD-GD1a. Image cross-correlationspectroscopy (ICCS) is used to further quantitatively characterizethis clustering by demonstrating that it occurs due to binding ofvirus to the dispersed population of NBD-GD1a.

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Wijsen, N., A. Aran, J. Pomoell, and S. Poedts. "Modelling three-dimensional transport of solar energetic protons in a corotating interaction region generated with EUHFORIA." Astronomy & Astrophysics 622 (January 28, 2019): A28. http://dx.doi.org/10.1051/0004-6361/201833958.

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Aims. We introduce a new solar energetic particle (SEP) transport code that aims at studying the effects of different background solar wind configurations on SEP events. In this work, we focus on the influence of varying solar wind velocities on the adiabatic energy changes of SEPs and study how a non-Parker background solar wind can trap particles temporarily at small heliocentric radial distances (≲1.5 AU) thereby influencing the cross-field diffusion of SEPs in the interplanetary space. Methods. Our particle transport code computes particle distributions in the heliosphere by solving the focused transport equation (FTE) in a stochastic manner. Particles are propagated in a solar wind generated by the newly developed data-driven heliospheric model, EUHFORIA. In this work, we solve the FTE, including all solar wind effects, cross-field diffusion, and magnetic-field gradient and curvature drifts. As initial conditions, we assume a delta injection of 4 MeV protons, spread uniformly over a selected region at the inner boundary of the model. To verify the model, we first propagate particles in nominal undisturbed fast and slow solar winds. Thereafter, we simulate and analyse the propagation of particles in a solar wind containing a corotating interaction region (CIR). We study the particle intensities and anisotropies measured by a fleet of virtual observers located at different positions in the heliosphere, as well as the global distribution of particles in interplanetary space. Results. The differential intensity-time profiles obtained in the simulations using the nominal Parker solar wind solutions illustrate the considerable adiabatic deceleration undergone by SEPs, especially when propagating in a fast solar wind. In the case of the solar wind containing a CIR, we observe that particles adiabatically accelerate when propagating in the compression waves bounding the CIR at small radial distances. In addition, for r ≳ 1.5 AU, there are particles accelerated by the reverse shock as indicated by, for example, the anisotropies and pitch-angle distributions of the particles. Moreover, a decrease in high-energy particles at the stream interface (SI) inside the CIR is observed. The compression/shock waves and the magnetic configuration near the SI may also act as a magnetic mirror, producing long-lasting high intensities at small radial distances. We also illustrate how the efficiency of the cross-field diffusion in spreading particles in the heliosphere is enhanced due to compressed magnetic fields. Finally, the inclusion of cross-field diffusion enables some particles to cross both the forward compression wave at small radial distances and the forward shock at larger radial distances. This results in the formation of an accelerated particle population centred on the forward shock, despite the lack of magnetic connection between the particle injection region and this shock wave. Particles injected in the fast solar wind stream cannot reach the forward shock since the SI acts as a diffusion barrier.

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