具有衰减扰动的耦合非线性振荡器中的共振
Resonance in coupled nonlinear oscillators with decaying perturbations
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中文总结 AI 辅助
研究非自治扰动对两个耦合非线性非相同振荡器系统的影响，耦合强度和扰动强度随时间按幂律衰减。通过平均法与李雅普诺夫函数构造导出非自治模型系统，分析锁相状态下共振解稳定性，并用非相同杜芬振荡器系统验证理论结果。
中文摘要 AI 辅助
研究了非自治扰动对两个耦合的非线性非相同振荡器系统的影响。假设耦合强度和扰动强度都根据幂律随时间衰减。我们关注在某些能量水平下与振荡器固有频率的可公度性相关的共振效应。特别地，描述了扰动和耦合参数的条件，在这些条件下出现锁相解，且振荡器能量渐近地接近共振水平。通过将平均方法与李雅普诺夫函数的构造相结合，导出了一个控制扰动动力学的非自治模型系统，并分析了锁相状态下共振解的稳定性。针对具有衰减耦合的非相同杜芬振荡器系统说明了理论结果。
英文摘要
The influence of nonautonomous perturbations on a system of two coupled nonlinear non-identical oscillators is studied. Both the coupling intensity and the perturbation strength are assumed to decay in time according to a power law. We focus on resonance effects associated with the commensurability of the natural frequencies of the oscillators at some energy levels. In particular, we describe the conditions on perturbations and coupling parameters under which phase-locked solutions appear with the oscillator energies remaining asymptotically close to resonant levels. By combining the averaging method with the construction of Lyapunov functions, we derive a nonautonomous model system governing the perturbed dynamics and analyse the stability of resonant solutions in the phase-locking regime. The theoretical results are illustrated for a system of non-identical Duffing oscillators with decaying coupling.
