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Zbl 1244.35158
Datsko, B.; Gafiychuk, V.
Complex nonlinear dynamics in subdiffusive activator-inhibitor systems. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 17, No. 4, 1673-1680 (2012). ISSN 1007-5704

Summary: In this article we analyze the linear stability of nonlinear time-fractional reaction-diffusion systems. As an example, the reaction-subdiffusion model with cubic nonlinearity is considered. By linear stability analysis and computer simulation, it was shown that fractional derivative orders can change substantially an eigenvalue spectrum and significantly enrich nonlinear system dynamics. A overall picture of nonlinear solutions in subdiffusive reaction-diffusion systems is presented.

MSC 2000:: *35R11
35K57 Reaction-diffusion equations
35B35 Stability of solutions of PDE

Keywords: reaction-diffusion system; fractional differential equations; homogeneous oscillations; dissipative structures

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Zentralblatt MATH Berlin [Germany]