Analytical estimates of the effect of amplitude modulated signal in nonlinearly damped Duffing-vander Pol oscillator

The effect of amplitude modulated (AM) signal on horseshoe chaos is studied both analytically and numerically in nonlinearly damped Duffing-vander Pol (DVP) oscillator. We assume the nonlinear damping term is proportional to the power of velocity (x˙) in the form |x˙|p−1. Using the Melnikov analytical method, the analytical threshold condition for the prediction of onset of horseshoe chaos is obtained. Melnikov threshold curves are drawn in different external parameters space. Our results show that as the damping exponent p increases from a small value, the threshold value for the onset of horseshoe is decreased. The analytical results are verified by numerical simulations using the computation of stable and unstable manifolds of saddle, measuring the time elapsed between two successive transverse intersections, bifurcation diagram, maximal Lyapunov exponent, phase portrait and Poincare´ map.