Study of Oscillations in Non-linear Systems by Linear Differential Equations with Periodic Coefficients

Abstract

In this paper a method has been developed to study the transient behaviour in non-linear systems in the vicinity of steady state oscillations. In the neighbourhood of steady state oscillations, other than equilibrium, the transient response of a non-linear system can be investigated by approximating the nonlinear differential equations describing the system by linear differential equations with periodic coefficients^2,4 and the stability of the periodic regimes^3,5 can be effectively studied. The theoretical formulation presented in this paper yields certain advantages over other existing methods including that given by Cosgriff².