The buffering phenomenon in a resonance hyperbolic boundary-value problem in radiophysics

By the buffering phenomenon we mean the existence of sufficiently many stable cycles in a system of differential equations with distributed coefficients. In systems of parabolic reaction-diffusion equations this interesting phenomenon was first discovered by numerical methods in [1] in which a problem in ecology was studied. It was then explained theoretically in [2] and [3]. The buffering phenomenon is of current interest, for example, in connection with the modelling of memory processes and the creation of memory cells [4]. It is therefore interesting to find simple radiophysical devices with this property. In the present paper we consider a mathematical model of such a device (an $\operatorname{RCLG}$-oscillator) and, with the aid of a suitable modification of the methods developed in [5], we study the problem of existence and stability of its periodic solutions.