Quasi-periodic oscillations in the system of three coupled van der Pol oscillators

Abstract

In this paper, we discuss quasi-periodic oscillations in the system of three dissipatively coupled van der Pol oscillators by the KAM method. In order to use this method, we apply the idea of the averaging method to the original system and obtain some normal form in which the frequency map satisfies a weaker nondegeneracy condition instead of the usual one. Then, it is proved that the system has quasi-periodic invariant 3-tori for most of the parameter set where its averaged system possesses invariant 3-tori. Our result verifies some numerical phenomena of Emelianova et al. (2013, 2014).