Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators

•We model the dynamics of dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators.•We give evidence that in the case of small positive or negative damping there exist two different types of transient chaos.•We confirm experimentally our numerical results.

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.