New methods for the investigation of periodic solutions in ring systems of unidirectionally coupled oscillators

Abstract

We consider special systems of ordinary differential equations, namely, ring systems of unidirectionally coupled oscillators. A new method is developed for the investigation of the problem of the existence and stability of periodic solutions for this class of systems. The specific feature of this approach is the use of certain auxiliary delay systems for the determination of cycles and for the analysis of their properties. The proposed method is illustrated by a specific example.