Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion. Issue 3 (29th June 2020) - Datsko, Bohdan
Summary: In this article, we analyze conditions for different types of instabilities and complex dynamics that occur in nonlinear two‐component incommensurate fractional reaction‐diffusion systems. It is shown that the stability and subsequent evolution of steady‐state solutions are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative orders. The results of the linear stability analysis are confirmed by computer simulations of the FitzHugh‐Nahumo and Brusselator models. On the basis of these models, it is demonstrated that the conditions of instability and pattern formation dynamics in fractional activator‐inhibitor systems can be quite different from the standard ones. As a result, a richer and more complicated spatiotemporal dynamics takes place in FRD systems. A common picture of possible nonlinear solutions in nonlinear time‐fractional incommensurate two‐component systems is presented.