Local methods in predicting occurrence of chaos in two-well potential systems: Superharmonic frequency region

Approximate criteria for chaos in two-well potential systems excited by harmonic force are considered. The excitation frequency is assumed to be close to 0·5 the natural frequency of the Small Orbit: i.e., close to the second order superharmonic resonance. Computer simulations reveal a scenario of transition to chaos significantly different from that at the principal resonance. Here both periodic attractors, of the Small and Large Orbits, lose stability and jointly turn into a strange attractor. Classical analytical approximate techniques are applied to analyze approximate periodic solutions and their higher order instabilities. The symmetry breaking instabilities of the Large Orbit and the first order instability of the approximate non-resonant Small Orbit solution are used to estimate the parameter region in which chaos may occur.