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Modal Series Method for Nonautonomous Nonlinear Systems

Nonlinear system analysis and design have been attracting increasing adherents in recent decades. Different normal form techniques, approximation methods, and perturbation procedures have been used to analyze these systems. In recent years, a novel approach, called modal series method, has been introduced and used to study the behavior of autonomous nonlinear dynamic systems of the form x = g(x). In this paper, we extend this approach to a wide class of nonautonomous nonlinear systems of the form x = g(x,i). Using two textbook examples, we show the capability of this extension to find approximate solutions for nonautonomous nonlinear systems.