A Numerical Investigation of Phase-Locked and Chaotic Behavior of Coupled Van Der Pol Oscillators

Abstract

Abstract This paper presents the results of numerical simulations of the dynamics of a pair of linearly coupled van der Pol oscillators. A four-dimensional parameter space (including the displacement and velocity coupling strengths and the detuning in addition to the usual non-linearity parameter of the uncoupled van der Pol oscillator) is explored. In addition to corroboration of analytical results for the existence and stability of the in-phase and out-of-phase modes, regions in the parameter space are obtained where stable phase-locked motions exist with phase differences other than 0° or 180°. The dependence of stable phase lag on parameter values is presented for representative portions of the parameter space. A region is also located where trajectories are obtained which provide the first evidence of chaotic behavior and strange at tractors in this system of unforced non-conservative oscillators.