Bistable chaos without symmetry in generalized synchronization

Abstract

Frequently, multistable chaos is found in dynamical systems with symmetry. We demonstrate a rare example of bistable chaos in generalized synchronization (GS) in coupled chaotic systems without symmetry. Bistable chaos in GS refers to two chaotic attractors in the response system which both synchronize with the driving dynamics in the sense of GS. By choosing appropriate coupling, the coupled system could be symmetric or asymmetric. Interestingly, it is found that the response system exhibits bistability in both cases. Three different types of bistable chaos have been identified. The crisis bifurcations which lead to the bistability are explored, and the relation between the bistable attractors is analyzed. The basin of attraction of the bistable attractors is extensively studied in both parameter space and initial condition space. The fractal basin boundary and the riddled basin are observed and they are characterized in terms of the uncertainty exponent.