Oscillons, kinks and patterns in a model for a periodically forced medium

Abstract

A dynamic model is devised for the patterns arising in a periodically forced extended medium. This model is based on the assumption of nearest pattern interaction approximation, and contains two control parameters alpha, beta. While beta controls the number of stable equilibrium states of the system. alpha serves as a coupling constant for an interaction of a localized excitation with its neighbors. Despite its extreme simplicity, the model provides a unified perspective of the formation of the patterns such as oscillons, linear and decorated kinks. kink to stripe transitions, skew-varicose and crossroll instabilities, etc. (C) 2002 Elsevier Science B.V. All rights reserved.