PATTERN FORMATION IN FRACTIONAL REACTION-DIFFUSION SYSTEMS WITH MULTIPLE HOMOGENEOUS STATES

This paper is devoted to the investigation of self-organization phenomena in time-fractional reaction-diffusion systems with multiple homogeneous states. It is shown that the fractional reaction-diffusion systems possess some new properties compared to the systems with derivatives of integer orders. In particular, some complex spatio-temporal solutions that cannot be found in the standard reaction-diffusion systems are identified. The simulation results are presented for the case of a incommensurate time-fractional reaction-diffusion system with a cubic nonlinearity.