Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force

The homoclinic bifurcation and transition from regular to asymptotic chaos in Duffing oscillator subjected to an amplitude modulated force is studied both analytically and numerically. Applying the Melnikov analytical method, the threshold condition for the occurrence of horseshoe chaos is obtained. Melnikov threshold curves are drawn in different external parameters space. Analytical predictions are demonstrated through direct numerical simulations. Parametric regimes where suppression of horseshoe chaos occurs are predicted. Period doubling route to chaos, intermittency route to chaos and quasiperiodic route to chaos are found to occur due to the amplitude-modulated force. Numerical investigations including computation of stable and unstable manifolds of saddle, maximal Lyapunov exponent, Poincaré map and bifurcation diagrams are used to detect homoclinic bifurcation and chaos.