Bifurcation and transitional dynamics in three-coupled oscillators with hard type nonlinearity

In this paper, we investigate various bifurcation and related dynamics of certain periodic attractors in a three-coupled oscillator system with hard type nonlinearity. The periodic attractors exist for comparatively large ε(=parameter showing the degree of nonlinearity), and they disappear via saddle-node (S-N) bifurcation when ε becomes small. Sometimes, there exist a heteroclinic and a homoclinic cycle near the bifurcation parameter value. In such cases, a quasi-periodic attractor appears generally after the S-N bifurcation. In particular, it presents intermittent phenomenon just after the S-N bifurcation. We clarify the existence of the heteroclinic and homoclinic cycles by drawing an unstable manifold of saddles on the Poincare section, and demonstrate the intermittent phenomenon by simulation.