Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems

Abstract

The paper considers the problem of determining the conditions under which a nonlinear dynamical system can give rise to a chaotic behaviour. On the basis of the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, two practical methods are presented for predicting the existence and the location of chaotic motions. This is formulated as a function of the system parameters, when the system structure is fixed by rather general input-output or state equation models. Several examples of application are presented to show the rather straightforward computations involved in the proposed methods, the kind of results which can be obtained and, due to the heuristic approach to the problem, their corresponding approximation. © 1992.