Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point

Abstract

Abstract In this article, we study complex spatio-temporal solutions in nonlinear time-fractional reaction-diffusion systems. The main attention is paid to nonlinear dynamics near a bifurcation point. Despite the fact that the homogeneous state is stable at the parameters lower than bifurcation ones, a variety of complex solutions can also form in the subcritical domain. As an example, we consider a generalized fractional FitzHugh-Nagumo model. Depending on the given standard bifurcation parameters and the order of fractional derivative, the new types of steady auto-wave solutions in such systems have revealed. By computer simulation, it is shown that fractional reaction-diffusion possess much more complex nonlinear dynamics than their integer counterparts even at a subcritical bifurcation.