THE INTERPLAY OF UNCORRELATED NOISE AND SMALL WORLD EFFECT ON PATTERN FORMATION IN TWO-DIMENSIONAL COUPLED MAP LATTICES

Abstract

By using a neuron-like map model to denote the generic dynamics of excitable systems, Gaussian-noise-induced pattern formation in the two-dimensional coupled map lattices with nearest-neighbor coupling and shortcut links has been studied. Given the appropriate initial values and parameter regions, with all nodes concerned, the functions of δ(n), χ and ℜ are introduced to analyze the evolution of pattern formation. It is found that there exists a critical εc beyond which the stable rotating spiral wave will appear. After introducing the Gaussian noise for the homogeneous ε region, different spatiotemporal stable patterns will be achieved. Additionally, the importance of the parameter I on the coupling strength C is discussed.