延迟系统中的反常行为
Anomalous Behavior in Systems with Delay
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中文总结 AI 辅助
本文研究时间延迟反馈系统中的反常行为，发现混沌解在非双曲不动点附近被捕获导致反常扩散与弱混沌，并探讨了恒定延迟及周期性调制延迟下该行为的机制与模型。
中文摘要 AI 辅助
在最近的一封信中[Phys. Rev. E 112, L042201 (2025)]，我们证明了在具有线性瞬时项和非线性延迟项的某类时间延迟反馈系统中，会出现反常扩散、弱混沌和弱遍历性破缺。这种反常行为是由混沌解在函数空间中接近非双曲不动点解时被捕获所致。在本文中，我们扩展了先前的研究，给出了更详细的见解，并展示了令人惊讶的新结果。我们首先研究恒定延迟的情况，在这种情况下，此类捕获事件期间的动力学行为可以通过中心流形理论来解释。在大延迟极限下，由于混沌相位的高有效维数，捕获事件的概率变得很小。因此，反常行为只能在非常大的时间尺度上观察到。通过引入延迟时间的周期性调制，捕获事件随着调制幅度的增加而变得更有可能发生，这是因为有效维数的减少和层流混沌的出现。对于较大的调制幅度值，反常行为更加复杂，其最相关的方面可以通过二维迭代映射和随机模型来重现。
英文摘要
In a recent letter [Phys. Rev. E 112, L042201 (2025)], we demonstrated the occurrence of anomalous diffusion, weak chaos, and weak ergodicity breaking in a certain class of time-delayed feedback systems with linear instantaneous and nonlinear delayed term. This anomalous behavior is caused by the trapping of chaotic solutions close to nonhyperbolic fixed-point solutions in function space. In this paper, we extend our previous study, present more detailed insights, and show surprising new results. We first investigate the case of a constant delay, where the dynamical behavior during such trapping events can be explained by center manifold theory. In the large-delay limit, the probability for the trapping events becomes small because of a high effective dimension of the chaotic phases. As a consequence, anomalous behavior is only observable on very large time scales. By introducing a periodic modulation of the delay time, trapping events become more probable with increasing modulation amplitude due to a reduction of the effective dimension and the occurrence of laminar chaos. For large values of the modulation amplitude, the anomalous behavior is more complex and the most relevant aspects can be reproduced by a two-dimensional iterated map and a stochastic model.
发表机构
- Chemnitz University of Technology（开姆尼茨工业大学）
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