Homoclinic and heteroclinic chaos in a triple-well oscillator

Abstract Holmes-Melnikov criteria for chaotic vibrations of a non-linear oscillator having three stable and two unstable equilibrium positions are obtained in analytic form. The chaotic threshold for homoclinic and heteroclinic bifurcations is studied as a function of two parameters: the frequency ω of the driving term, and the ratio between the stable and unstable equilibrium positions[formula]. It is shown that the limits[formula]connect with two related Duffing and anti-Duffing type oscillators. For a set of parameter values in the region of particular interest, excellent agreement is obtained between the theoretical predictions and numerical calculations. Additionally, as[formula]ever-longer-lasting intermittent transient motion is observed at[formula]—the most chaotic frequency for homoclinic bifurcation.