Effect of amplitude-modulated excitation on the dynamic behaviors in an externally driven Rayleigh-van der Pol-Duffing system

The influence of the low-frequency amplitude-modulated excitation on the dynamic behaviors in an externally driven Rayleigh-van der Pol-Duffing system (EDRVDS) is investigated theoretically and numerically. First, we propose two bursting oscillation types of the EDRVDS without the low-frequency amplitude-modulated excitation and explore their mechanisms by using the fast/slow decomposition analysis. Then, by regarding the low-frequency cosine function as a generalized slow variable, we transform the driven EDRVDS into a formal autonomous nonlinear equation. Next, we investigate the influence of the low-frequency amplitude-modulated excitation on the two bursting oscillations from the perspectives of the coefficient n equals to odd and even numbers, respectively. Especially, some detailed problems, such as the ups and downs in the stable equilibrium sets, the ups and downs in the shapes of the limit cycles, symmetric and asymmetric of the bifurcation structures, are explored clearly. By this effort, we realize the amplitude-modulation of the oscillations in the excited states and silent states successfully. Moreover, we have the aid of the theoretical analysis and numerical simulations to guarantee the preciseness of the analysis results.