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

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 α,β. While β controls the number of stable equilibrium states of the system, α 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.