Regularity–Partial Chaos–Regularity Transition and Overlapped KAM Scenarios in a Conservative System of Two Linearly Coupled Double-Well Oscillators

Abstract

For linearly coupled double-well oscillators the regularity–partial chaos–regularity transition is found. First, an incomplete KAM scenario develops with increasing energy, from integrable pattern comprising in-phase and out-of-phase small elliptic orbits towards a partial chaos, with a deformed regular island immersed in a chaotic sea. At a critical energy a new deformed island appears as a mirror image. Above the critical energy the inverse KAM scenario leads to gradual destruction of partial chaos and to the appearance of large elliptic orbits which correspond to the large-amplitude limit governed by uncoupled oscillators with cubic anharmonicities.