Horseshoe Dynamics in an Asymmetric Duffing-Van der Pol Oscillator Driven by a Narrow-Band Frequency Modulated Force

Abstract

We investigate both analytically and numerically the occurrence of horseshoe chaos in three different asymmetric Duffing-Van der Pol oscillators driven by a narrow-band frequency modulated force f(cos ωt-g sin Ωt sin ωt). We identify the regions of horseshoe chaos in (ω = Ω; f) parameter space and bring out the effect of the parameter α. We present the results for α = 0.9 and 1.2 in the three systems. When g = 0 and for fixed values of the other parameters there are regions in the (α, f) plane where (i) the horseshoe chaos can occur in both the x ＜ 0 and x ＞ 0 regions, and (ii) no horseshoe dynamics occurs in both the x ＜ 0 and x ＞ 0 regions. We illustrate that by varying the parameter g one can suppress chaotic dynamics, say, in the x ＞ 0 region or induce chaos in the region x ＜ 0. This is realized in the three asymmetrical systems.