Chaos due to homoclinic and heteroclinic orbits in two coupled oscillators with nonisochronism

Abstract

We show that chaotic dynamics occur in a pair of weakly nonlinear coupled active oscillators when nonisochronism, the dependence of oscillation frequencies on amplitudes, is included. The strange attractor in this system develops from a nearby homoclinic orbit, the same mechanism that leads to chaos in coupled active-passive modes. After analytically determining the most likely parameter region for such a homoclinic orbit, we found the neighboring region of chaos predicted by Shilnikov’s theorem. These coupled oscillators also exhibit multistability and unexpected three-frequency oscillations.