New Riddling Bifurcation in Asymmetric Dynamical Systems

We investigate the bifurcation mechanism for the loss of transverse stability of the chaotic attractor in an invariant subspace in an asymmetric dynamical system. It is found that a direct transition to global riddling 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. This new bifurcation mechanism differs from that in symmetric dynamical systems. After such a riddling bifurcation, the basin becomes globally riddled with a dense set of repelling tongues leading to divergent orbits. This riddled basin is also characterized by divergence and uncertainty exponents, and typical power-law scaling is found.