School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India.
Chaos. 2013 Mar;23(1):013136. doi: 10.1063/1.4793542.
We report our investigation on the effect of multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a low- and a high-frequency periodic force. For the single oscillator, we obtain analytical expressions for the response amplitude Q and the amplitude g of the high-frequency force at which resonance occurs. The regions in parameter space of enhanced Q at resonance, as compared to the case in absence of time-delay, show a bands-like structure. For the two-coupled oscillators, we explain all the features of variation of Q with the control parameter g. For the system of n-coupled oscillators with a single time-delay coupling, the response amplitudes of the oscillators are shown to be independent of the time-delay. In the case of a multi time-delayed coupling, undamped signal propagation takes place for coupling strength (δ) above a certain critical value (denoted as δu). Moreover, the response amplitude approaches a limiting value QL with the oscillator number i. We obtain analytical expressions for both δu and QL.
我们报告了关于多个时滞对单 Duffing 振子和由 n 个 Duffing 振子组成的系统中振动共振的影响的研究，这些振子通过低频和高频周期性力单向耦合。对于单振子，我们得到了响应幅度 Q 和发生共振时高频力的幅度 g 的解析表达式。与无时滞情况相比，在共振时增强 Q 的参数空间区域表现出带状结构。对于两个耦合振子，我们解释了 Q 随控制参数 g 的变化的所有特征。对于具有单个时滞耦合的 n 个耦合振子系统，振子的响应幅度与时滞无关。在多时间延迟耦合的情况下，对于耦合强度（δ）高于某个临界值（表示为 δu），无阻尼信号传播发生。此外，响应幅度随着振子数量 i 趋近于一个极限值 QL。我们得到了 δu 和 QL 的解析表达式。
