Complex nonlinear dynamics in subdiffusive activator–inhibitor systems

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.

► Stability of subdiffusive reaction–diffusion system is analyzed.
► Conditions for time and spatial pattern formation are determined.
► It was shown that fractional derivative orders change substantially an eigenvalue spectrum and nonlinear system dynamics.
► A overall picture of nonlinear solutions in subdiffusive regime is presented.