Application of an Equivalent Nonlinear System Approach to Dissipative Dynamical Systems

Abstract

This paper deals with a method for generating approximate periodic solutions for dissipative second-order nonlinear systems. The approach presented is based on the definition of an auxiliary nonlinear system which is equivalent to the original system in the sense of minimum mean-square difference. The method is applied to a system with a cubic nonlinearity and leads to a substantial improvement over more conventional first-order approximation techniques.