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Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators. (English) Zbl 1329.37037

Summary: The dynamics of two coupled, dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators has been studied. We give numerical and experimental (circuit implementation) evidence that in the case of small positive or negative damping there exist two different types of transient chaos. After the decay of the transient chaos in the neighborhood of chaotic saddle we observe the transient chaos in the neighborhood of unstable tori. We argue that our results are robust and they exist in the wide range of system parameters.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70H08 Nearly integrable Hamiltonian systems, KAM theory
94C05 Analytic circuit theory
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