Riddling Transition in Unidirectionally Coupled Systems Woochang Lim

Riddling Transition in Unidirectionally Coupled Systems Woochang Lim and Sang-Yoon Kim Department of Physics Kangwon National University Unidirectionally-Coupled System without Symmetry A Chaotic Attractor (CA) on the Invariant Line Investigation of Its Transverse Stability in terms of Periodic Saddles Embedded in the CA 1

Riddling Transition Through A Transcritical Contact Bifurcation Disappearance of an absorbing area through a transcritical contact bifurcation between a periodic saddle (△) embedded in the CA and a repeller (▽) on the basin boundary for Formation of a dense set of “repelling tongues, ” leading to divergent orbits 2

Globally-Riddled Basin of Attraction For , CA with Globally-Riddled Basin The measure of the riddled basin decreases to zero as b goes to a blow-out bifurcation point. For , CA Chaotic saddle 3

Characterization of The Riddled Basin by The Uncertainty Exponents : Probability that and lead to different final states As , becomes smaller. The uncertainty in determining the final state increases. 4

Summary Direct Global-Riddling Transition through The Transcritical Contact Bifurcation between A Periodic Saddle Embedded in The CA and A Repeller on The Basin Boundary Disappearance of The Absorbing Area Basin riddled with a dense set of repelling tongues, leading to divergent orbits. Characterization of The Riddled Basin by The Uncertainty exponents As (the blow-out bifurcation point) the value of becomes smaller. The uncertainty in determining the final state increases. 5