Статті в журналах: "Dynamical system modeling"

1

Bors, Dorota, and Robert Stańczy. "Dynamical system modeling fermionic limit." Discrete & Continuous Dynamical Systems - B 23, no. 1 (2018): 45–55. http://dx.doi.org/10.3934/dcdsb.2018004.

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2

Dmitriev, Andrey, Olga Tsukanova, and Svetlana Maltseva. "Modeling of Microblogging Social Networks: Dynamical System vs. Random Dynamical System." Procedia Computer Science 122 (2017): 812–19. http://dx.doi.org/10.1016/j.procs.2017.11.441.

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3

JANSSON, JOHAN, CLAES JOHNSON, and ANDERS LOGG. "COMPUTATIONAL MODELING OF DYNAMICAL SYSTEMS." Mathematical Models and Methods in Applied Sciences 15, no. 03 (March 2005): 471–81. http://dx.doi.org/10.1142/s0218202505000431.

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In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 10–9 computed over the time interval [0,100], and a lattice consisting of large and small point masses.

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4

Runolfsson, Thordur. "Towards hybrid system modeling of uncertain complex dynamical systems." Nonlinear Analysis: Hybrid Systems 2, no. 2 (June 2008): 383–93. http://dx.doi.org/10.1016/j.nahs.2006.05.004.

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5

Redondo, J. M., D. Ibarra-Vega, J. Catumba-Ruíz, and M. P. Sánchez-Muñoz. "Hydrological system modeling: Approach for analysis with dynamical systems." Journal of Physics: Conference Series 1514 (March 2020): 012013. http://dx.doi.org/10.1088/1742-6596/1514/1/012013.

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6

Frankel, Michael L., Gregor Kovačič, Victor Roytburd, and Ilya Timofeyev. "Finite-dimensional dynamical system modeling thermal instabilities." Physica D: Nonlinear Phenomena 137, no. 3-4 (March 2000): 295–315. http://dx.doi.org/10.1016/s0167-2789(99)00180-3.

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7

Nasim, Imran, and Michael E. Henderson. "Dynamically Meaningful Latent Representations of Dynamical Systems." Mathematics 12, no. 3 (February 2, 2024): 476. http://dx.doi.org/10.3390/math12030476.

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Dynamical systems are ubiquitous in the physical world and are often well-described by partial differential equations (PDEs). Despite their formally infinite-dimensional solution space, a number of systems have long time dynamics that live on a low-dimensional manifold. However, current methods to probe the long time dynamics require prerequisite knowledge about the underlying dynamics of the system. In this study, we present a data-driven hybrid modeling approach to help tackle this problem by combining numerically derived representations and latent representations obtained from an autoencoder. We validate our latent representations and show they are dynamically interpretable, capturing the dynamical characteristics of qualitatively distinct solution types. Furthermore, we probe the topological preservation of the latent representation with respect to the raw dynamical data using methods from persistent homology. Finally, we show that our framework is generalizable, having been successfully applied to both integrable and non-integrable systems that capture a rich and diverse array of solution types. Our method does not require any prior dynamical knowledge of the system and can be used to discover the intrinsic dynamical behavior in a purely data-driven way.

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8

ABEL, MARKUS. "NONPARAMETRIC MODELING AND SPATIOTEMPORAL DYNAMICAL SYSTEMS." International Journal of Bifurcation and Chaos 14, no. 06 (June 2004): 2027–39. http://dx.doi.org/10.1142/s0218127404010382.

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This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated data. As an application, the example of vortex ripple dynamics, a highly complex fluid-granular system, is treated.

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9

Jian, Shen, Han Feng, Chen Fang, Zhou Qiao, and Pavel M. Trivailo. "Dynamics and modeling of rocket towed net system." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232, no. 1 (October 13, 2016): 185–97. http://dx.doi.org/10.1177/0954410016673090.

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In order to study the complex dynamical behavior of the rocket towed net system, a three-dimensional model consisting of a rigid rocket model and a lumped mass net model is built based on the aerodynamics theory. The rocket towed net system model is solved by the fourth-order Runge–Kutta method in simulation. Simulation and experimental results show that the accuracies of rocket towed net system expanding distance were about 90% of the system length. With the comparison of simulation, a rigid multibody model and experimental results in rocket mass center trajectory, velocity, and pitch angle, the dynamical characteristics of rocket towed net system have been basically studied. It illustrates that the lumped mass model simulates the real rocket towed net system flying test better than the rigid multibody model. It also shows that the dynamical parameters of rocket towed net system flight have an impact on the system in the whole flying process. Constitutive model of flexible net mesh-belts can be considered in the future research studies.

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10

Hahn, Luzia, and Peter Eberhard. "Transient Dynamical-Thermal-Optical System Modeling and Simulation." EPJ Web of Conferences 238 (2020): 12001. http://dx.doi.org/10.1051/epjconf/202023812001.

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In this work, methods and procedures are investigated for the holistic simulation of the dynamicalthermal behavior of high-performance optics like lithography objectives. Flexible multibody systems in combination with model order reduction methods, finite element thermal analysis and optical system analyses are used for transient simulations of the dynamical-thermal behavior of optical systems at low computational cost.

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11

Goldenstein, Siome, Edward Large, and Dimitris Metaxas. "Non-linear dynamical system approach to behavior modeling." Visual Computer 15, no. 7-8 (November 1999): 349–64. http://dx.doi.org/10.1007/s003710050184.

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12

Maluf, David A., Jiming Liu, and Michel C. Desmarais. "Consistent dynamical system observers for nondeterministic event modeling." Information Sciences 94, no. 1-4 (October 1996): 41–53. http://dx.doi.org/10.1016/0020-0255(96)00136-3.

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13

Wang, Xiaoyan, Tong Li, and Jinghua Yao. "Dynamical behaviors of a system modeling wave bifurcations." Communications in Mathematical Sciences 16, no. 7 (2018): 1869–94. http://dx.doi.org/10.4310/cms.2018.v16.n7.a6.

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14

Tandy, Marvin, and Marcus Wono Setya Budhi. "Dynamical System Modeling in Asset and Liability Management." ITM Web of Conferences 75 (2025): 02009. https://doi.org/10.1051/itmconf/20257502009.

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Insurance companies must ensure a balance between the profits generated from their investment and the liabilities they owe to policyholders. This is widely known as asset and liability management (ALM). One important element of ALM involves forecasting the long-term financial status of the company. Therefore, a discrete time dynamical system is developed to illustrate the fluctuations in the financial components of an insurance company. Subsequently, simulations are conducted based on the constructed model for cases both with and without mortality. The model takes into account varying premium amounts and durations, a stochastic capital market, a dynamic management strategy, as well as mechanisms for establishing reserves. The financial components arising in the model are calculated recursively, allowing for easier and more efficient simulations.

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15

Saha, S., S. Nadiga, C. Thiaw, J. Wang, W. Wang, Q. Zhang, H. M. Van den Dool, et al. "The NCEP Climate Forecast System." Journal of Climate 19, no. 15 (August 1, 2006): 3483–517. http://dx.doi.org/10.1175/jcli3812.1.

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Abstract The Climate Forecast System (CFS), the fully coupled ocean–land–atmosphere dynamical seasonal prediction system, which became operational at NCEP in August 2004, is described and evaluated in this paper. The CFS provides important advances in operational seasonal prediction on a number of fronts. For the first time in the history of U.S. operational seasonal prediction, a dynamical modeling system has demonstrated a level of skill in forecasting U.S. surface temperature and precipitation that is comparable to the skill of the statistical methods used by the NCEP Climate Prediction Center (CPC). This represents a significant improvement over the previous dynamical modeling system used at NCEP. Furthermore, the skill provided by the CFS spatially and temporally complements the skill provided by the statistical tools. The availability of a dynamical modeling tool with demonstrated skill should result in overall improvement in the operational seasonal forecasts produced by CPC. The atmospheric component of the CFS is a lower-resolution version of the Global Forecast System (GFS) that was the operational global weather prediction model at NCEP during 2003. The ocean component is the GFDL Modular Ocean Model version 3 (MOM3). There are several important improvements inherent in the new CFS relative to the previous dynamical forecast system. These include (i) the atmosphere–ocean coupling spans almost all of the globe (as opposed to the tropical Pacific only); (ii) the CFS is a fully coupled modeling system with no flux correction (as opposed to the previous uncoupled “tier-2” system, which employed multiple bias and flux corrections); and (iii) a set of fully coupled retrospective forecasts covering a 24-yr period (1981–2004), with 15 forecasts per calendar month out to nine months into the future, have been produced with the CFS. These 24 years of fully coupled retrospective forecasts are of paramount importance to the proper calibration (bias correction) of subsequent operational seasonal forecasts. They provide a meaningful a priori estimate of model skill that is critical in determining the utility of the real-time dynamical forecast in the operational framework. The retrospective dataset also provides a wealth of information for researchers to study interactive atmosphere–land–ocean processes.

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16

BOLLT, ERIK. "ATTRACTOR MODELING AND EMPIRICAL NONLINEAR MODEL REDUCTION OF DISSIPATIVE DYNAMICAL SYSTEMS." International Journal of Bifurcation and Chaos 17, no. 04 (April 2007): 1199–219. http://dx.doi.org/10.1142/s021812740701777x.

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In a broad sense, model reduction means producing a low-dimensional dynamical system that replicates either approximately, or more strictly, exactly and topologically, the output of a dynamical system. Model reduction has an important role in the study of dynamical systems and also with engineering problems. In many cases, there exists a good low-dimensional model for even very high-dimensional systems, even infinite dimensional systems in the case of a PDE with a low-dimensional attractor. The theory of global attractors approaches these issues analytically, and focuses on finding (depending on the question at hand), a slow-manifold, inertial manifold, or center manifold, on which a restricted dynamical system represents the interesting behavior of the dynamical system; the main issue depends on defining a stable invariant manifold in which the dynamical system is invariant. These approaches are analytical in nature, however, and are therefore not always appropriate for dynamical systems known only empirically through a dataset. Empirically, the collection of tools available are much more restricted, and are essentially linear in nature. Usually variants of Galerkin's method, project the dynamical system onto a function linear subspace spanned by modes of some chosen spanning set. Even the popular Karhunen–Loeve decomposition, or POD, method is exactly such a method. As such, it is forced to either make severe errors in the case that the invariant space is intrinsically a highly nonlinear manifold, or bypass low-dimensionality by retaining many modes in order to capture the manifold. In this work, we present a method of modeling a low-dimensional nonlinear manifold known only through the dataset. The manifold is modeled as a discrete graph structure. Intrinsic manifold coordinates will be found specifically through the ISOMAP algorithm recently developed in the Machine Learning community originally for purposes of image recognition.

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17

Liane Vina G. Ocampo. "Modeling Stock Market Dynamics in the Philippines Through Symbolic Dynamical System." Journal of Information Systems Engineering and Management 10, no. 12s (February 19, 2025): 197–202. https://doi.org/10.52783/jisem.v10i12s.1774.

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The study employs the theory of symbolic dynamical system in modelling stock market in the Philippines. Precisely stock market modeling process is complex and dynamic. The main objective of this paper is to build a model using the following factors namely; peso dollar exchange rate, inflation rate, GDP, un employment rate. These factors are assumed to be the indicators of the Philippine stock market. In this study we derived the mathematical model of each of those factors. The output of this paper can build a possible programming system or software for forecasting stock market predictions to be more accessible and more accurate since various machine learning approaches have been applied in stock market prediction.

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18

BENTZEN, N. C. K., A. M. ZHABOTINSKY, and J. L. LAUGESEN. "MODELING OF GLUTAMATE-INDUCED DYNAMICAL PATTERNS." International Journal of Neural Systems 19, no. 06 (December 2009): 395–407. http://dx.doi.org/10.1142/s0129065709002105.

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Based on established physiological mechanisms, the paper presents a detailed computer model, which supports the hypothesis that temporal lobe epilepsy may be caused by failure of glutamate reuptake from the extracellular space. The elevated glutamate concentration causes an increased activation of NMDA receptors in pyramidal neurons, which in turn leads to neuronal dynamics that is qualitatively identical to epileptiform activity. We identify by chaos analysis a surprising possibility that muscarinergic receptors can help the system out of a chaotic regime.

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19

Corner, Sebastien, Corina Sandu, and Adrian Sandu. "Modeling and sensitivity analysis methodology for hybrid dynamical system." Nonlinear Analysis: Hybrid Systems 31 (February 2019): 19–40. http://dx.doi.org/10.1016/j.nahs.2018.07.003.

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20

Maeda, Hiroshi, Shinichiro Asaoka, and Shuta Murakami. "Dynamical fuzzy reasoning and its application to system modeling." Fuzzy Sets and Systems 80, no. 1 (May 1996): 101–9. http://dx.doi.org/10.1016/0165-0114(95)00130-1.

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21

HERNANDEZ-ROMERO, NORBERTO, JUAN CARLOS SECK-TUOH-MORA, MANUEL GONZALEZ-HERNANDEZ, JOSELITO MEDINA-MARIN, and JUAN JOSE FLORES-ROMERO. "MODELING A NONLINEAR LIQUID LEVEL SYSTEM BY CELLULAR NEURAL NETWORKS." International Journal of Modern Physics C 21, no. 04 (April 2010): 489–501. http://dx.doi.org/10.1142/s0129183110015245.

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This paper presents the analogue simulation of a nonlinear liquid level system composed by two tanks; the system is controlled using the methodology of exact linearization via state feedback by cellular neural networks (CNNs). The relevance of this manuscript is to show how a block diagram representing the analogue modeling and control of a nonlinear dynamical system, can be implemented and regulated by CNNs, whose cells may contain numerical values or arithmetic and control operations. In this way the dynamical system is modeled by a set of local-interacting elements without need of a central supervisor.

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22

Kulkov, V. M., Yu G. Egorov, S. O. Firsyuk, V. V. Terentyev, and A. O. Shemyakov. "Modeling the angular momentum control of small spacecraft with a magnetic attitude control system." Доклады Академии наук 484, no. 4 (May 5, 2019): 415–19. http://dx.doi.org/10.31857/s0869-56524844415-419.

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The problem of modeling the angular momentum control modes of small spacecraft using electromagnetic systems interacting with the Earth’s magnetic field is considered. The electromagnetic system control law has been constructed for various compositions of measurable parameters. A set of scale factors has been formed to investigate the angular momentum control mode of dynamically similar models. Based on a dynamical test stand, we have carried out experimental studies to model the angular motion dynamics of small spacecraft with a magnetic attitude control system.

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23

Liu, Guang Yu, Hai Xia Ren, An Ke Xue, and Guo Qiang Shen. "Modeling of a Multiple Effect Desalination System." Applied Mechanics and Materials 448-453 (October 2013): 3519–22. http://dx.doi.org/10.4028/www.scientific.net/amm.448-453.3519.

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A multiple variable model is developed for a multiple-effect low temperature desalination system. Multiple-effect water desalination has been used in industry for decades due to its high efficiency and high quality of fresh water production. Here, its dynamical process is modeled based on the mass and heat conservation laws and then expressed in terms of a state space equation, enabling people to carry out analysis and design controllers.

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24

Bin Salamah, Yasser A. "Non-smooth Modeling and Variable Structure Control of a Class of Hybrid Dynamical Systems." Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012108. http://dx.doi.org/10.1088/1742-6596/2090/1/012108.

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Abstract In this work, we propose a modeling formulation and controller design for a class of hybrid dynamical systems. In this formulation, a switching dynamical system is modeled as a dynamical system with discontinuous right hand side. More specifically, the system is transformed to a nonlinear system with discontinuous nonlinearities. Then, a synthesis of feedback linearization and sliding mode control is employed for output tracking control problem. Application and implementation of this approach is illustrated via a chemical process example.

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25

Cheng, Sen, and Philip N. Sabes. "Modeling Sensorimotor Learning with Linear Dynamical Systems." Neural Computation 18, no. 4 (April 1, 2006): 760–93. http://dx.doi.org/10.1162/neco.2006.18.4.760.

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Recent studies have employed simple linear dynamical systems to model trial-by-trial dynamics in various sensorimotor learning tasks. Here we explore the theoretical and practical considerations that arise when employing the general class of linear dynamical systems (LDS) as a model for sensorimotor learning. In this framework, the state of the system is a set of parameters that define the current sensorimotor transformation— the function that maps sensory inputs to motor outputs. The class of LDS models provides a first-order approximation for any Markovian (state-dependent) learning rule that specifies the changes in the sensorimotor transformation that result from sensory feedback on each movement. We show that modeling the trial-by-trial dynamics of learning provides a sub-stantially enhanced picture of the process of adaptation compared to measurements of the steady state of adaptation derived from more traditional blocked-exposure experiments. Specifically, these models can be used to quantify sensory and performance biases, the extent to which learned changes in the sensorimotor transformation decay over time, and the portion of motor variability due to either learning or performance variability. We show that previous attempts to fit such models with linear regression have not generally yielded consistent parameter estimates. Instead, we present an expectation-maximization algorithm for fitting LDS models to experimental data and describe the difficulties inherent in estimating the parameters associated with feedback-driven learning. Finally, we demonstrate the application of these methods in a simple sensorimotor learning experiment: adaptation to shifted visual feedback during reaching.

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26

Skrinjar, Luka, Janko Slavič, and Miha Boltežar. "Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System." Strojniški vestnik - Journal of Mechanical Engineering 63, no. 7-8 (July 17, 2017): 417. http://dx.doi.org/10.5545/sv-jme.2017.4561.

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The design process for dynamical models has to consider all the properties of a mechanical system that have an effect on its dynamical response. In multi-body dynamics, flexible bodies are frequently modeled as rigid, resulting in non-valid modeling of the pre-stress effect. In this research a focus on the pre-stress effect for a flexible body assembled in a rigid-flexible multibody system is presented. In a rigid-flexible assembly a flexible body is modeled with an absolute nodal coordinate formulation (ANCF) of finite elements. The geometrical properties of the flexible body are evaluated based on the frequency response and compared with the experimental values. An experiment including the pre-stress effect and large displacements is designed and the measured values of the displacement are compared to the numerical results in order to validate the dynamical model. The pre-stress was found to be significant for proper numerical modeling. The partially validated numerical model was used to research the effect of different parameters on the dynamical response of a pre-stressed, rigid-flexible assembly.

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27

Альаззави, А. Ш. М., and Д. К. Андрейченко. "MODELING OF NONLINEAR STABILIZATION SYSTEM." Южно-Сибирский научный вестник, no. 1(41) (February 28, 2022): 10–16. http://dx.doi.org/10.25699/sssb.2022.41.1.005.

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Саратовский национальный исследовательский государственный университет имени Н.Г. Чернышевского, г. СаратовРанее методами теории комбинированных динамических систем (КДС) были исследованы области устойчивости спутников с упруго деформируемыми элементами конструкции, и был реализован параметрический синтез по линеаризованной модели с учетом времени запаздывания в исполнительных органах систем стабилизации. В настоящей работе по результатам численного моделирования спутников с упруго деформируемыми элементами конструкции показано, что нелинейная КДС с запаздыванием в исполнительных органах системы управления может быть стабилизирована в результате параметрического синтеза по линеаризованной модели. Previously, the stability regions of satellites with elastically deformable structural elements were investigated by the methods of the theory of hybrid dynamical systems (HDS), and parametric synthesis was realized by the linearized model taking into account the time lag in the stabilization system. In this paper, based on the results of numerical modeling of satellites with elastic-deformable structural elements, it is shown that the nonlinear HDS with a delay in the control system can be stabilized as a result of parametric synthesis by a linearized model.

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Chakraborty, Payel, Soumyendu Bhattacharjee, Arijit Roy, Jinia Datta, Kamal Kumar Ghosh, and Biswarup Neogi. "Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis." YMER Digital 21, no. 07 (July 18, 2022): 526–40. http://dx.doi.org/10.37896/ymer21.07/42.

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Any mechanical system can easily be analyzed with the help of proper designing or modeling. All kinematical constrains are also been considered at the time of modeling. Generally the traditional dynamical differential equations are solved to predict the nature of the system. In this work, some typical types of dynamical mechanical system in taken into consideration and further the dynamical equations are being solved using ‘Series Solutions Technique’ for the analysis of the nonlinear system. The solution is consisting of two sections. Using frequency response analysis via simulation, which section of the solution is more suitable or effective for the designing purpose has also been explained in detail. Finally, the local stability analysis of the entire system is studied in detail with proper numerical simulation. Keywords: Nonlinearity, Series Solution, Stability Analysis, Phase Portrait, Frequency Response Function.

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29

Altıntan, Derya, Vi̇lda Purutçuoğlu, and Ömür Uğur. "Impulsive Expressions in Stochastic Simulation Algorithms." International Journal of Computational Methods 15, no. 01 (September 27, 2017): 1750075. http://dx.doi.org/10.1142/s021987621750075x.

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Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous, and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact that stochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples.

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30

El Guezar, Fatima, and Hassane Bouzahir. "Chaotic Behavior in a Switched Dynamical System." Modelling and Simulation in Engineering 2008 (2008): 1–6. http://dx.doi.org/10.1155/2008/798395.

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We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator) which is a Scilab (scientific laboratory) package. The followed approach takes into account the hybrid nature of the circuit.

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31

GAO Jinggui, and FENG Enmin. "Nonlinear Enzyme-Catalytic Dynamical System Modeling of Microbial Continuous Fermentation." INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences 4, no. 10 (June 30, 2012): 400–407. http://dx.doi.org/10.4156/aiss.vol4.issue10.47.

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32

Shi, Xian Jin, Di Ping Wu, and Zhi Ying Gao. "Study on Dynamical Modeling of the Rolling Mill Vertical System." Advanced Materials Research 383-390 (November 2011): 4825–30. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.4825.

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Vertical vibration is universal in the vertical system of rolling mill. It has a seriously bad effect on the quality of strip. Dynamic model of the vertical system plays an important role in the analysis of vertical vibration in rolling mill. On the basis of 1420mm six roller cold rolling mill, ADAMS rigid model and flexibility model are established in this paper. Contact stiffness of rollers is calculated through ansys simulation. Contact stiffness between the work-roll and strip is calculated by using theoretical methods and stiffness of mill stand is calculated by simplifying mill stand structure. Natural frequency and some amplitude-frequency response of vertical vibration are analyzed. The test results prove that the modeling method is feasible. Vibration derived from the deformation of rolls can be observed directly in the flexible model, which can’t be realized in the rigid body model. At the same time, the new method of calculating vertical system stiffness is also proved to be reasonable.

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33

Timmermann, A., H. U. Voss, and R. Pasmanter. "Empirical Dynamical System Modeling of ENSO Using Nonlinear Inverse Techniques." Journal of Physical Oceanography 31, no. 6 (June 2001): 1579–98. http://dx.doi.org/10.1175/1520-0485(2001)031<1579:edsmoe>2.0.co;2.

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Golubyatnikov, V. P., and M. V. Kazantsev. "Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback." Journal of Mathematical Sciences 230, no. 1 (February 26, 2018): 46–54. http://dx.doi.org/10.1007/s10958-018-3725-0.

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35

Vesperini, E., S. E. Zepf, A. Kundu, and K. M. Ashman. "Modeling the Dynamical Evolution of the M87 Globular Cluster System." Astrophysical Journal 593, no. 2 (August 20, 2003): 760–71. http://dx.doi.org/10.1086/376688.

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36

Nasyrov, I. K., and V. V. Andreev. "Modeling of information channel by using of pseudorandom signals of nonlinear dynamical system." Power engineering: research, equipment, technology 22, no. 4 (November 15, 2020): 79–87. http://dx.doi.org/10.30724/1998-9903-2020-22-4-79-87.

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Pseudorandom signals of nonlinear dynamical systems are studied and the possibility of their application in information systems analyzed. Continuous and discrete dynamical systems are considered: Lorenz System, Bernoulli and Henon maps. Since the parameters of dynamical systems (DS) are included in the equations linearly, the principal possibility of the state linear control of a nonlinear DS is shown. The correlation properties comparative analysis of these DSs signals is carried out.. Analysis of correlation characteristics has shown that the use of chaotic signals in communication and radar systems can significantly increase their resolution over the range and taking into account the specific properties of chaotic signals, it allows them to be hidden. The representation of nonlinear dynamical systems equations in the form of stochastic differential equations allowed us to obtain an expression for the likelihood functional, with the help of which many problems of optimal signal reception are solved. It is shown that the main step in processing the received message, which provides the maximum likelihood functionals, is to calculate the correlation integrals between the components and the systems under consideration. This made it possible to base the detection algorithm on the correlation reception between signal components. A correlation detection receiver was synthesized and the operating characteristics of the receiver were found.

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37

Aledo, Juan A., Silvia Martinez, and Jose C. Valverde. "Parallel Dynamical Systems over Graphs and Related Topics: A Survey." Journal of Applied Mathematics 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/594294.

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In discrete processes, as computational or genetic ones, there are many entities and each entity has a state at a given time. The update of states of the entities constitutes an evolution in time of the system, that is, a discrete dynamical system. The relations among entities are usually represented by a graph. The update of the states is determined by the relations of the entities and some local functions which together constitute (global) evolution operator of the dynamical system. If the states of the entities are updated in a synchronous manner, the system is called aparallel dynamical system. This paper is devoted to review the main results on the dynamical behavior of parallel dynamical systems over graphs which constitute a generic tool for modeling discrete processes.

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38

Zaytsev, Anatoly, Vyacheslav Kravchenko, and Dashadondok Shirapov. "An approach to logical-mathematical computer modeling of linear and nonlinear dynamical systems." E3S Web of Conferences 583 (2024): 06014. http://dx.doi.org/10.1051/e3sconf/202458306014.

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The paper deals with the problem of modeling linear and nonlinear dynamical systems using information technologies and programming. The processes of modeling, synthesis and inference of solutions to problems are considered, and the possibility of their integration within the described approach is shown. The substantive aspects of the development of special mathematical and algorithmic support for the construction of a software system for the analysis and processing of expert information for the purposes of automated synthesis and inference of solutions are briefly outlined. The aim of the work is to create a new approach of logical-mathematical computer modeling of linear and nonlinear dynamical systems and to develop a prototype of a software computational expert system based on it. As a result of the research, a universal approach of logical-mathematical computer modeling of linear and nonlinear dynamical systems has been developed and proposed. The proposed approach can be used to organize the process of computer modeling and automated synthesis of task solutions with the output of their results. The mathematical model of the knowledge base and process of its construction for the selected subject area, as well as the algorithm for outputting solutions to problems with its software implementation in the Python programming language, are shown. Examples of solution output for various linear and nonlinear problems are given. The developed prototype of the software computational expert system using the proposed logical- mathematical approach will significantly simplify the process of modeling dynamical systems and make the solution of problems' simpler and more understandable.

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39

AMIGÓ, JOSÉ M., ÁNGEL GIMÉNEZ, FRANCISCO MORILLAS, and JOSÉ VALERO. "ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS." International Journal of Bifurcation and Chaos 20, no. 09 (September 2010): 2681–700. http://dx.doi.org/10.1142/s0218127410027295.

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In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.

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40

Liu, Xianming, Jinqiao Duan, Jicheng Liu, and Peter E. Kloeden. "Synchronization of Dissipative Dynamical Systems Driven by Non-Gaussian Lévy Noises." International Journal of Stochastic Analysis 2010 (February 23, 2010): 1–13. http://dx.doi.org/10.1155/2010/502803.

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Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation, and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under a class of Lévy noises is considered. After discussing cocycle property, stationary orbits, and random attractors, a synchronization phenomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity and integrability conditions. The synchronization result implies that coupled dynamical systems share a dynamical feature in some asymptotic sense.

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41

Leventides, John, and Costas Poulios. "Koopman Operators and the $3x+1$-Dynamical System." SIAM Journal on Applied Dynamical Systems 20, no. 4 (January 2021): 1773–813. http://dx.doi.org/10.1137/20m1348182.

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42

Leventides, John, and Costas Poulios. "Koopman Operators and the $3x+1$-Dynamical System." SIAM Journal on Applied Dynamical Systems 20, no. 4 (January 2021): 1773–813. http://dx.doi.org/10.1137/20m1348182.

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43

Nadar, Sreenivasan Rajamoni, and Vikas Rai. "Transient Periodicity in a Morris-Lecar Neural System." ISRN Biomathematics 2012 (July 1, 2012): 1–7. http://dx.doi.org/10.5402/2012/546315.

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The dynamical complexity of a system of ordinary differential equations (ODEs) modeling the dynamics of a neuron that interacts with other neurons through on-off excitatory and inhibitory synapses in a neural system was investigated in detail. The model used Morris-Lecar (ML) equations with an additional autonomous variable representing the input from interaction of excitatory neuronal cells with local interneurons. Numerical simulations yielded a rich repertoire of dynamical behavior associated with this three-dimensional system, which included periodic, chaotic oscillation and rare bursts of episodic periodicity called the transient periodicity.

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44

NAGARAJ, NITHIN. "HUFFMAN CODING AS A NONLINEAR DYNAMICAL SYSTEM." International Journal of Bifurcation and Chaos 21, no. 06 (June 2011): 1727–36. http://dx.doi.org/10.1142/s0218127411029392.

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In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture their essential information? We propose modeling stochastic sources as piecewise-linear discrete chaotic dynamical systems known as Generalized Luröth Series (GLS) which has its roots in Georg Cantor's work in 1869. These GLS are special maps with the property that their Lyapunov exponent is equal to the Shannon's entropy of the source (up to a constant of proportionality). By successively approximating the source with GLS having fewer states (with the nearest Lyapunov exponent), we derive a binary coding algorithm which turns out to be a rediscovery of Huffman coding, the popular lossless compression algorithm used in the JPEG international standard for still image compression.

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45

Li, Jian Jia, and Xin Hua Zhao. "Dynamics Modeling and Simulation of Tracked Five DOF Mobile Manipulator." Advanced Materials Research 433-440 (January 2012): 4817–22. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.4817.

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The dynamical analysis for the tracked moving platform and the manipulator are established based on by Newton-Euler method and Dynamics model is respectively obtained, Moreover, Dynamic simulation is conducted, and reveals the input-output relation for the motion system from dynamical simulation, and plays a solid basic for the further study of dynamic modeling and motion control.

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46

BELLOMO, NICOLA, BENEDETTO PICCOLI, and ANDREA TOSIN. "MODELING CROWD DYNAMICS FROM A COMPLEX SYSTEM VIEWPOINT." Mathematical Models and Methods in Applied Sciences 22, supp02 (July 25, 2012): 1230004. http://dx.doi.org/10.1142/s0218202512300049.

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This paper aims at indicating research perspectives on the mathematical modeling of crowd dynamics, pointing on the one hand to insights into the complexity features of pedestrian flows and on the other hand to a critical overview of the most popular modeling approaches currently adopted in the specialized literature. Particularly, the focus is on scaling problems, namely representation and modeling at microscopic, macroscopic, and mesoscopic scales, which, entangled with the complexity issues of living systems, generate multiscale dynamical effects, such as e.g. self-organization. Mathematical structures suitable to approach such multiscale aspects are proposed, along with a forward look at research developments.

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47

Yaakoubi, Hanen, and Joseph Haggège. "Modeling and simulation of the two-tank system within a hybrid framework." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 4 (August 1, 2023): 4222. http://dx.doi.org/10.11591/ijece.v13i4.pp4222-4233.

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<p><span lang="EN-US">Most real-world dynamical systems are often involving continuous behaviors and discrete events, in this case, they are called hybrid dynamical systems (HDSs). To properly model this kind of systems, it is necessary to consider both the continuous and the discrete aspects of its dynamics. In this paper, a modeling framework based on the hybrid automata (HA) approach is proposed. This hybrid modeling framework allows combining the multi-state models of the system, described by nonlinear diﬀerential equations, with the system’s discrete dynamics described by ﬁnite state machines. To attest to the efficiency of the proposed modeling framework, its application to a two-tank hybrid system (TTHS) is presented. The TTHS studied is a typical benchmark for HDSs with four operating modes. The MATLAB Simulink and Stateflow tools are used to implement and simulate the hybrid model of the TTHS. Different simulations results demonstrate the efficiency of the proposed modeling framework, which allows us to appropriately have a complete model of an HDS.</span></p>

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48

Hu, Zhenhua, and Wen Chen. "Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System." Discrete Dynamics in Nature and Society 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/275134.

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We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

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49

Kirillov, Alexander N., and Alexander M. Sazonov. "The global stability of the Schumpeterian dynamical system." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 16, no. 4 (2020): 348–56. http://dx.doi.org/10.21638/11701/spbu10.2020.401.

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In this article, we present the studies that develop Schumpeter’s theory of endogenous evolution of economic systems. An approach to modeling the limitation of economic growth due to the limitation of markets, resource bases and other factors is proposed. For this purpose, the concept of economic niche volume is introduced. The global stability of the equilibrium of the dynamical system with the Jacobi matrix having, at the equilibrium, all eigenvalues equal to zero, except one being negative, is proved. The proposed model makes it possible to evaluate and predict the dynamics of the development of firms in the economic sector.

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50

Kravets, Victor, Volodymyr Kravets, and Olexiy Burov. "Analytical Modeling of the Dynamic System of the Fourth Order." Transactions on Machine Learning and Artificial Intelligence 9, no. 3 (May 23, 2021): 14–24. http://dx.doi.org/10.14738/tmlai.93.9947.

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A canonical mathematical model of a fourth-order dynamical system in the form of A.M. Letov. The analytical modeling methods are based on the algebraic concept and the principle of symmetry. The symmetry principle is realized on the set of four indices of the roots of the characteristic equation and the set of four indices of the phase coordinates of the dynamic system. The problem of the quality of dynamic processes in time is reduced to the algebraic problem of distribution of four roots in the complex plane. An analogy is established in the procedure for transforming the characteristic determinant to a polynomial and elementary symmetric polynomials of four roots. On the basis of the theory of residues, a new form of analytical representation of data in time is obtained in the form of ordered determinants with respect to the indices of four roots and indices of four coordinates. General provisions are illustrated by a stochastic dynamical system in the form of an asymmetric Markov chain with four states and continuous time, which is described by the fourth-order Kolmogorov equations.

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