Mechanisms for the hard bubbling transition in symmetrically coupled chaotic systems

초록

We investigate mechanisms for the hard bubbling transition in symmetrically coupled one-dimensional maps. A transition from strong to weak synchronization occurs via a first period-doubling or pitchfork transverse bifurcation of a periodic saddle embedded in the synchronous chaotic attractor. The consequence of such transverse bifurcations depends on the existence of an 'absorbing area,' controlling the global dynamics. In the presence of an absorbing area, a subcritical transverse bifurcation is found to give rise to abrupt appearance of transient intermittent bursts with large amplitude. For this case, any small parameter mismatch that is unavoidable in real systems induces a hard bubbling transition via an interior crisis. Through a detailed numerical analysis, we present explicit examples for the subcritical period-doubling and pitchfork transverse bifurcations, leading to hard bubbling.