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

摘要

In this work, we consider a family of two-dimensional coupled sine maps. We providedetailed pictures and some general properties of the associated basin structures, the analysisof the global bifurcations which cause qualitative changes in the shape of chaotic attractorsand 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 problemmay become particularly challenging when the discrete dynamical system is represented by theiteration of a noninvertible map, because in this case nonconnected or multiply connected basinscan be obtained. Coexistence of synchronized and antisynchronized chaotic states [Maistrenkoet al., 2005].