Chaotic dynamics in Bonhoffer–van der Pol fractional reaction–diffusion system

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.