School of Physics, Bharathidasan University, Tiruchirapalli, Tamilnadu 620 024, India.
Chaos. 2011 Sep;21(3):033106. doi: 10.1063/1.3610213.
We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.
我们研究了多稳定态在低频和高频周期性驱动力作用下的周期性势系统中振动共振发生的作用。在这两种情况下，当高频力的振幅发生变化时，低频响应幅度会出现一系列共振峰，并趋近于一个极限值。我们使用一种理论方法，根据运动方程的平衡点的共振频率和稳定性来分析多共振的机制。在过阻尼系统中，响应幅度总是高于没有高频力的情况。然而，在欠阻尼系统中，只有当低频小于 1 时才会发生这种情况。在欠阻尼系统中，当慢振荡发生的平衡点处于最大稳定状态时，响应幅度最大，在跨临界分岔时最小。而在过阻尼系统中，响应幅度在跨临界分岔时最大，在关联平衡点处于最大稳定状态时最小。当势的周期性被截断时，系统只显示出几个共振峰。
