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

Abstract

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.