Chaotic boundary crisis in the Duffing Van der Pol Vibro-imapct oscillator

This paper investigates the chaotic boundary crisis in the Duffing Van der Pol Vibro-impact oscillator by the generalized cell mapping method using diagraph. The previous reports have shown that a chaotic boundary crisis dues to the collision of a chaotic attractor with a saddle on its basin boundary. We study computationally the curves of stable and unstable manifolds for the period saddle on the basin boundary when the crisis parameter passes the critical value. Our results reveal that the boundary crisis is associated with the tangency of the stable and unstable manifolds of period saddle.