Steady states in the twin-well potential oscillator: Computer simulations and approximate analytical studies.

The paper is focused on the phenomena of various steady-state oscillations exhibited by the twin-well potential system. Regions of existence of different attractors in the system parameter domain are examined and a picture book of different steady states for fixed damping and forcing is presented: 20 different combinations of single or coexisting, small orbit or large orbit, periodic and chaotic attractors are displayed. Computer simulations are followed by an approximate analytical analysis: A study of various forms of instability of periodic solutions gives close form approximate criteria for occurrence of T-periodic small orbit and large orbit oscillations, and for cross-well chaos.