A special bifurcation of riddled basin in two coupled skew tent maps

Abstract

A chaotic synchronized system of coupled skew tent maps is discussed. The locally and globally riddled basins of the chaotic synchronized attractor are studied. It is found that the coupling parameter values corresponding to the locally riddled basin are isolated points embedded in the coupling parameter intervals of the globally riddled basin. This kind of bifurcation is novel and not like the local–global riddling bifurcation in found other references. We believe this bifurcation will be generic in systems, whose chaotic attractors are close to the attractive basins’ boundaries infinitely, despite discrete or differential systems.