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

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 some model problems, which are a kind of invariant. Informative examples from radiophysics are considered