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Complex nonlinear dynamics in subdiffusive activator-inhibitor systems |
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| Authors: | B Datsko V Gafiychuk |
| Institution: | a Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Naukova Street 3 B, Lviv 79060, Ukraine b SGT Inc., 7701 Greenbelt Rd Suite 400 Greenbelt, MD 20770, USA c NASA Ames Research Center, Moffett Field, CA 94035-1000, USA |
| Abstract: | 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. |
| Keywords: | Reaction-diffusion system Fractional differential equations Homogeneous oscillations Dissipative structures |
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