Multi-stability and basin crisis in synchronized parametrically driven oscillators

摘要: This paper studies the synchronization dynamics of two linearly coupled parametrically excited oscillators. The Lyapunov stability theory is employed to obtain some sufficient algebraic criteria for global asymptotic systems, and an estimated critical coupling, k cr, which could be observed determined. transition found associated with boundary crisis chaotic attractor. In bistable states, where asymmetric T-periodic attractors co-exist, we show that oscillators can attain multi-stability via a new dynamical transition—the basin wherein co-existing are destroyed while created. steady states examined possible bifurcation routes identified.