Pattern formation in oscillatory media: Beyond reaction-diffusion model

Abstract

Reaction-diffusion models of active media provide a quite general framework for describing pattern formation phenomena in very different systems. Here, we extend this model and show that in oscillatory systems more complex oscillatory wave patterns might emerge based on different locally coupled interactions. Autonomous, two-layer Cellular Neural/Nonlinear Network models are used and spatial interactions are encoded in coupling rules. The properties of emerging oscillatory patterns can be determined in advance from the analysis of the coupling rules and cell dynamics.