SUPERCRITICAL PITCHFORK BIFURCATION OF THE QUASI-PERIODIC SWITCHING SOLUTION IN A RING OF SIX-COUPLED, BISTABLE OSCILLATORS

Abstract

In our preceding study, we investigated the appearance and disappearance scenario of (quasi-periodic) switching solution in a ring of six-coupled, bistable oscillators. This system was expressed as twelve-dimensional phase space, which was divided into linear subspace H and its complimentary linear subspace H⊥. We investigated the stability of switching solution in H by calculating the conditional Lyapunov exponent to the direction of H⊥. As a result, we found a critical coupling factor αcrt at which switching solution lost its stability in the direction of H⊥. However, we did not know what type of bifurcation occurred at this point. In this study, we elucidate that switching solution causes a supercritical pitchfork bifurcation at αcrt.