Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as limiting case of differential advection

摘要

A one-component bistable reaction-diffusion system with asymmetric nonlocalcoup ling is derived as limiting case of a two-component activator-inhibitorreaction -diffusion model with differential advection. The effects ofasymmetric nonlocal couplings in such a bistable reaction-diffusi on system arethen compared to the previously studied case of a system with symm etricnonlocal coupling. We carry out a linear stability analysis of the spatiallyhomogeneous steady sta tes of the model and numerical simulations of the modelto show how the asymmetr ic nonlocal coupling controls and alters the steadystates and the front dynamic s in the system. In a second step, a third fastreaction-diffusion equation is included which ind uces the formation of morecomplex patterns. A linear stability analysis predicts traveling waves forasymmetric nonlocal coupling in contrast to a stationary Turing patterns for asystem with symmetric nonlocal coupling. These findings are verified by directnumerical integration of the full equations with nonlocal coupling.