一类记忆非线性系统的极限环与混沌
Limit Cycles and Chaos Induced by a Nonlinearity with Memory
摘要：
受光学谐振腔非线性响应中分布时延观测的启发，我们研究了噪声驱动的机械振荡器中类似时延的影响。对于一个延迟时间是相称的逆耗散率，我们找到稳定的极限环。对于较长的延迟，我们发现了一个政权的混沌动力学与双涡卷吸引子。我们还分析了时间延迟对振荡器的频谱和振荡幅度的影响。我们的研究结果指出了新的机会，非线性能量收集，提供了一个非线性分布的时间延迟可以在机械系统中实现。
英文摘要：
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the inverse dissipation rate, we find stable limit cycles. For longer delays, we discover a regime of chaotic dynamics associated with a double scroll attractor. We also analyze the effects of time delay on the spectrum and oscillation amplitude of the oscillator. Our results point to new opportunities for nonlinear energy harvesting, provided that a nonlinearity with distributed time delay can be implemented in mechanical systems.
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