Front and Turing patterns induced by Mexican-hat–like nonlocal feedback
Institut für Theoretische Physik, Technische Universität Berlin - Hardenbergstraße 36, 10623 Berlin, Germany
Received: 23 November 2014
Accepted: 10 February 2015
We consider the effects of a Mexican-hat–shaped nonlocal spatial coupling, i.e., symmetric long-range inhibition superimposed with short-range excitation, upon front propagation in a model of a bistable reaction-diffusion system. We show that the velocity of front propagation can be controlled up to a certain coupling strength beyond which spatially periodic patterns, such as Turing patterns or coexistence of spatially homogeneous solutions and Turing patterns, may be induced. This behaviour is investigated through a linear stability analysis of the spatially homogeneous steady states and numerical investigations of the full nonlinear equations in dependence upon the nonlocal coupling strength and the ratio of the excitatory and inhibitory coupling ranges.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 82.40.Ck – Pattern formation in reactions with diffusion, flow and heat transfer
© EPLA, 2015