Global Effect of Transverse Bifurcations in Coupled Chaotic Systems

초록

We investigate the global effect of transverse bifurcations in symmetrically coupled one-dimensional maps. A transition from strong to weak synchronization occurs via a first transverse bifurcation of a periodic saddle embedded in a synchronous chaotic attractor (SCA). For the case of a supercritical transverse bifurcation, a soft bubbling transition occurs. On the other hand, a subcritical transverse bifurcation leads to a hard transition. The global effect of such subcritical hard bifurcations are found to depend on whether they may or may not induce a "contact" between the SCA and its basin boundary. For the case of a "contact" bifurcation, an absorbing area, surrounding the SCA and acting as a bounded trapping vessel, disappears; hence, basin riddling occurs. However, for the case of a "non-contact" bifurcation, such an absorbing area is preserved; hence, hard bubbling takes place. Through a detailed numerical analysis, we give explicit examples for all kinds of transverse bifurcations leading to bubbling and riddling.

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