Bistable chaotic family and its chaotic mechanism

Abstract

The emergence of many chaotic families shows that chaos can be generated by deterministic approaches. From the perspective of the mechanism of chaos, we add the opposite time-delayed effects to an overdamped bistable system to obtain chaos. The effect of time delay is determined by the change of the optimal window which origin from logical stochastic resonance. A variety of chaotic systems with different chaotic attractors are obtained by different combinations of opposite effects. Furthermore, we propose the mechanism of chaos in time-delayed bistable systems, that is, the opposite time-delayed effects lead to repeated increasing and decreasing in depth of potential wells. This mechanism is verified by constructing a force-free Duffing equation with an oscillatory double-well potential. Results show that the bistable systems can form bistable chaotic family based on the same chaos generation mechanism.