Abstract
Abstract The effect of nonlinear damping including fractional damping on the onset of horseshoe chaos is studied both analytically and numerically in the double-well Duffing–Vander Pol (DVP) oscillator driven by various sinusoidal forces. The sinusoidal type periodic forces of our interest are sine wave, rectified sine wave, and modulus of sine wave. Using the Melnikov analytical method, the threshold condition for the onset of horseshoe chaos is obtained for each sinusoidal force. Melnikov threshold curves are drawn in (f,\;ω) parameters space for each force. When the damping component (p) increases from a small value, the Melnikov threshold value ( f M ) $(f_{M})$ is decreased for each force. Suppression of horseshoe chaos is predicted due to the effect of weak periodic perturbation and nonlinear fractional damping. Analytical predictions are demonstrated through direct numerical simulations.
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