Mathematical modeling of different types of instabilities in time fractional reaction-diffusion systems. (English) Zbl 1189.35151

Gafiychuk, V.; Datsko, B.

Comput. Math. Appl. 59, No. 3, 1101-1107 (2010).

Summary: We investigate possible scenarios of pattern formations in reaction-diffusion systems with time fractional derivatives. Linear stability analysis is performed for different values of derivative orders. Results of qualitative analysis are confirmed by numerical simulations of specific partial differential equations. Most attention is paid to two models: a fractional order reaction diffusion system with Bonhoeffer-van der Pol kinetics and to the Brusselator model.

MSC:

35K57	Reaction-diffusion equations
35R11	Fractional partial differential equations
26A33	Fractional derivatives and integrals
45K05	Integro-partial differential equations

Keywords:

reaction-diffusion system; fractional differential equations; inhomogeneous oscillations; dissipative structures

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