Abstract
We study the behavior of nonlinear bistable systems as the parameters are slowly perturbed periodically. Using averaged equations, typical features of the transition from regular to chaotic dynamics are determined in an externally driven Duffing oscillator and in a system consisting of a van der Pol and a linear oscillator coupled resonantly. We find that general features of the transition to chaos in these models are in many respects similar. In both systems considered, chaotic regions, arising due to similar mechanisms, are situated inside or near the regions of bistability.
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