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Chaotic dynamics in Bonhoffer-van der Pol fractional reaction-diffusion system |
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| Authors: | B.Y. Datsko V.V. Gafiychuk |
| Affiliation: | a Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences, Naukova 3b, Lviv 79063, 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 fractional reaction-diffusion systems. As an example, the reaction-diffusion model with cubic nonlinearity is considered. By computer simulation, it was shown that in such simplest system, a complex nonlinear dynamics, which includes spatially non-homogeneous oscillations and spatio-temporal chaos, takes place. Possible applications of the fractional reaction-diffusion system for signal processing and pattern recognition systems are presented. |
| Keywords: | Fractional differential equation Anomalous diffusion Reaction-diffusion Pattern formation Pattern recognition Chaotic dynamics Applications |
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