Riddling transition in asymmetric dynamical systems

초록

We investigate the bifurcation mechanism for the loss of transverse stability of the chaotic at tractor on art invariant subspace in the asymmetric dynamical system. It is found that a direct global-riddling transition occurs through a transcritical contact bifurcation between a periodic saddle embedded in the chaotic attractor on the invariant subspace and a repeller on its basin boundary. At the moment of this new type of riddling bifurcation, a bounded trapping region, called an absorbing area, disappears. Consequently, the basin becomes globally riddled with a dense set of repelling tongues leading: to divergent orbits. This riddled basin is also characterized by the uncertainty exponents, and thus typical power-law scaling is found.

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