具有自诱导随机共振的快慢系统中的随机周期轨道
Stochastic periodic orbits in fast-slow systems with self-induced stochastic resonance
摘要：
噪声在各种系统中普遍存在。在多时间尺度的系统中，噪声可以引起各种相干行为。自诱导随机共振（SISR）是一种典型的噪声诱导的现象，在这样的系统中，其中噪声作用于快速子系统引起的随机共振类边界穿越。本文分析了快慢系统中由SISR引起的随机周期轨道。通过引入向边界的平均第一通过速度的概念，建立了一个距离匹配条件，通过该条件可以计算边界穿越的临界转捩位置。相应地，通过将动力学粘在慢流形上，可以得到理论上的随机周期轨道。结果表明，即使在大噪声情况下，理论预测与分段线性FitzHugh-Nagumo系统的蒙特卡罗模拟结果也非常吻合。此外，所提出的方法扩展到原来的FitzHugh-Nagumo系统，也发现表现出一致的精度。这些结果为揭示快慢系统中的相干行为机制提供了新的思路，并将对更复杂的复杂系统和大型网络中的相干行为提供新的思路.
英文摘要：
Noise is ubiquitous in various systems. In systems with multiple timescales, noise can induce various coherent behaviors. Self-induced stochastic resonance (SISR) is a typical noise-induced phenomenon identified in such systems, wherein noise acting on the fast subsystem causes stochastic resonancelike boundary crossings. In this paper, we analyze the stochastic periodic orbits caused by SISR in fast-slow systems. By introducing the notion of the mean first passage velocity toward the boundary, a distance matching condition is established, through which the critical transition position of boundary crossing can be calculated. The theoretical stochastic periodic orbit can be accordingly obtained via gluing the dynamics along the slow manifolds. It is shown that the theoretical predictions are in excellent agreement with the results of Monte Carlo simulations for a piecewise linear FitzHugh-Nagumo system even for large noise. Furthermore, the proposed method is extended to the original FitzHugh-Nagumo system and also found to exhibit consistent accuracy. These results provide insights into the mechanisms of coherent behaviors in fast-slow systems and will shed light on the coherent behaviors in more complex systems and large networks.
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