Intermittent switching for three repulsively coupled oscillators

We study intermittent switching behaviors in a system with three identical oscillators coupled diffusively and repulsively, to clarify a bifurcation scenario which generates such intermittent switching behaviors. We use the Stuart-Landau oscillator, which is a general form of Hopf bifurcation, and can describe both cases: limit cycle and inactive (i.e., non-self-oscillatory) cases. From a numerical study of the bifurcation structure, two different routes to chaos which has S3 symmetry were found. One is the sudden appearance of chaos as Pomeau-Manneville intermittency, which is found for the inactive case. In this case a trajectory shows switching among three mutually symmetric tori when a parameter exceeds critical value. The other route, which appears for the limit cycle case, consists of two parts: First, chaos with lower symmetry appears through period doubling, and after the two successive attractor-merging crises, chaos which has S3 symmetry appears. At each crisis, the attractor changes its symmetry.