A Bifurcation Approach to the Synchronization of Coupled Van der Pol Oscillators

Abstract

We undertake a bifurcation analysis of a velocity coupled system of two classical nonidentical Vander Pol oscillators to understand the appearance and structure of 1:kparameter regions with syn-chronized states as we vary the coupling and the frequency mismatch. These regions include multi-stability of solutions and are formed by classical tongues bordered by curves of limit point bifurcationof periodic orbits with an isola structure and an additional subregion surrounded by curves of torusbifurcations and a curve characterized by a geometrical tangency condition. Symmetry argumentsexplain the difference between the even and oddkcases.