The buffer property in resonance systems of non-linear hyperbolic equations

Abstract

We study hyperbolic boundary-value problems for systems of telegraph equations with non-linear boundary conditions at the endpoints of a finite interval. The buffer property is established, that is, the existence of an arbitrary given finite number of stable time-periodic solutions for appropriately chosen parameter values, for this class of systems. For the case of a resonance spectrum of eigenfrequencies, the study of self-induced oscillations in various systems is shown to lead to one of the following two model problems, which are a kind of invariant: 0;$ SRC=http://ej.iop.org/images/0036-0279/55/2/R02/tex_rm_268_img1.gif/>??Informative examples from radiophysics are considered.