In this paper, we study the nonlinear response of a bistable van der Pol–Mathieu–Duffing (VMD) oscillator under the influence of two periodic excitations of widely different frequencies. We have shown that by systematically modulating the strength of the high-frequency drive as well as the strength of the parametric oscillation, a symmetrically oscillating bistable potential can be converted to a symmetrically oscillating monostable potential. In addition to this effect, the strength of the fast drive modifies the damping as well, allowing us to define a threshold value of this strength at which a supercritical Hopf bifurcation occurs. All analytical results have shown to be numerically consistent.

在本文中，我们研究了双稳态 van der Pol-Mathieu-Duffing (VMD) 振荡器在频率差异很大的两种周期性激发的影响下的非线性响应。我们已经证明，通过系统地调制高频驱动的强度以及参数振荡的强度，对称振荡的双稳态电位可以转换为对称振荡的单稳态电位。除了这种影响之外，快速驱动的强度也会改变阻尼，使我们能够定义发生超临界 Hopf 分叉时该强度的阈值。所有的分析结果都表明在数值上是一致的。