An efficient and fully explicit model to simulate delayed activator–inhibitor systems with anomalous diffusion

Macías‐Díaz, Jorge E.

doi:10.1007/s10910-019-01046-9

Cited by 5 publications

(2 citation statements)

References 47 publications

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“…The space derivatives can mainly influence on spatial location, smooth and mobility of appearing dissipative structures. That confirms the results of computer simulation 31‐34 . Last time, a number of papers have been published on the study of self‐organization phenomena in RDS with space fractional derivatives.…”

Section: Linear Stability Analysissupporting

confidence: 79%

Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion

Datsko

2020

Comp and Math Methods

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Summary In this article, we analyze conditions for different types of instabilities and complex dynamics that occur in nonlinear two‐component incommensurate fractional reaction‐diffusion systems. It is shown that the stability and subsequent evolution of steady‐state solutions are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative orders. The results of the linear stability analysis are confirmed by computer simulations of the FitzHugh‐Nahumo and Brusselator models. On the basis of these models, it is demonstrated that the conditions of instability and pattern formation dynamics in fractional activator‐inhibitor systems can be quite different from the standard ones. As a result, a richer and more complicated spatiotemporal dynamics takes place in FRD systems. A common picture of possible nonlinear solutions in nonlinear time‐fractional incommensurate two‐component systems is presented.

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Section: Linear Stability Analysissupporting

confidence: 79%

Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion

Datsko

2020

Comp and Math Methods

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“…In addition, finite difference methods for solving the unsteady and steady state problems are provided. Finite difference method has been shown to be powerful for solving various problems [31,32,33,34,35], which also include mathematical chemistry areas [36,37,38,39,40,41,42,43,44,45].…”

Section: Introductionmentioning

confidence: 99%

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Mungkasi

2020

2020 3rd International Seminar on Research of Information Technology and Intelligent Systems (ISRITI)

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Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion

2019

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Auto-wave solutions in nonlinear time-fractional reaction-diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction-diffusion systems, we generalized two classical activator-inhibitor nonlinear models: FitzHugh-Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activatorinhibitor systems is presented.

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An efficient and fully explicit model to simulate delayed activator–inhibitor systems with anomalous diffusion

Cited by 5 publications

References 47 publications

Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion

Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion

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