Dynamics of Coupled Van der Pol Oscillators

Abstract

In this paper, we consider the problem on the synchronization of two or three Van der Pol oscillators in the case where the oscillators are identical and constraints between them are weak. The existence and stability of two types of periodic solutions are studied under the assumption that constraints between the oscillators are dissipative or active. The analysis of the problem is based on methods of the qualitative theory of differential equations, namely, the method of integral manifolds and the method of normal Poincaré–Dulac forms. The problem is reduced to the study of normal forms. We used a version of the Krylov–Bogolyubov algorithm, which allows one to obtain asymptotic formulas for periodic solutions.