Asymptotic Behavior of the Solutions of a System of Two Weakly Coupled Relaxation Oscillators with Delayed Feedback

Abstract

We consider a dynamic system that consists of two coupled self-excited oscillators with delayed feedback. Such models occur in applied problems of radio physics and optics. It is assumed that the nonlinear function, which is responsible for the feedback, is finite and contains a great parameter. This reveals the possibility to use a special analytical method to study relaxation oscillations. It is shown that the dynamics of two such oscillators in the case of their asymptotically weak coupling is described by a special finite-dimension mapping and can be rather sophisticated.