Basins and Critical Curves Generated by A Family of Two-Dimensional Sine Maps

Abstract: In this work, we consider a family of two-dimensional coupled sine maps. We provide detailed pictures and some general properties of the associated basin structures, the analysis of the global bifurcations which cause qualitative changes in the shape of chaotic attractors and in the topological structure of the basins is carried out by the method of critical curves. We give the complex phenomena riddled and intermingled basins of attraction. This problem may become particularly challenging when the discrete dynamical system is represented by the iteration of a noninvertible map, because in this case nonconnected or multiply connected basins can be obtained. Coexistence of synchronized and antisynchronized chaotic states [Maistrenko et al., 2005]