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

We study hyperbolic boundary-value problems for systems of telegraph equati ons with non-linear boundary conditions at the endpoints of a finite interv al. The buffer property is established, that is, the existence of an arbitr ary given finite number of stable time-periodic solutions for appropriately chosen parameter values, for this class of systems. For the case of a reso nance spectrum of eigenfrequencies, the study of self-induced oscillations in various systems is shown to lead to one of the following two model probl ems, which are a kind of invariant: partial derivative (2)w/partial derivativet partial derivativex = w + lambd a>(*) over bar * (1 - w(2)) partial derivativew/partial derivativex, w(t,x + 1) = -w(t,x), lambda >0; partial derivativew/partial derivativet + a(2) partial derivative (3)w/part ial derivativex(3) = w-w(3), w(t,x + 1) = -w(t,x), a not equal 0. Informative examples from radiophysics are considered.