DISSIPATIVE BIDIMENSIONAL SYSTEMS AND RESONANT EXCITATIONS

This paper deals with the most important characteristics of a generic bidimensional dissipative system, subject to a small external excitati on in resonance or in quasi-resonance with the primary resonance frequ ency of the system. In particular, the appearance of limit cycles and bifurcations is considered, by means of an asymptotic perturbation met hod quite different from the standard perturbation theory. We demonstr ate that its behavior looks like the behavior of a universal model sys tem. In view of it, we identify a sufficient condition to obtain a dou bly periodic motion, when a second little frequency appears, in additi on to the primary resonance frequency. Comparison with the numerical s olution obtained by the Runge-Kutta-Fehlberg method confirms the valid ity of our analysis. (C) 1997 Elsevier Science Ltd.