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Complex nonlinear dynamics in subdiffusive activator-inhibitor systems. (English) Zbl 1244.35158
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:
35R11Fractional partial differential equations
35K57Reaction-diffusion equations
35B35Stability of solutions of PDE
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