极限环、复Floquet乘子和固有噪声
Limit cycles, complex Floquet multipliers and intrinsic noise
摘要：
研究了内禀噪声对化学反应系统的影响，该系统在确定性极限下以振荡的方式逼近极限环。以往的研究表明，系统的振荡方法的一个固定点的噪声可以转换的振荡衰减到持续的相干振荡与大幅度。当稳定吸引子是极限环时，也会产生类似的效应。我们计算了几个模型系统的关联函数和频谱特性的波动在适当的共同移动Frenet框架，包括驱动和耦合的振荡器，和Willamowski-Roessler系统。数值模拟结果令人信服地证实了分析结果。该效应是相当普遍的，并且每当控制极限环稳定性的Floquet乘数是复杂的时发生，随着接近不稳定边界，振荡的振幅增加。
英文摘要：
We study the effects of intrinsic noise on chemical reaction systems, which in the deterministic limit approach a limit cycle in an oscillatory manner. Previous studies of systems with an oscillatory approach to a fixed point have shown that the noise can transform the oscillatory decay into sustained coherent oscillations with a large amplitude. We show that a similar effect occurs when the stable attractors are limit cycles. We compute the correlation functions and spectral properties of the fluctuations in suitably co-moving Frenet frames for several model systems including driven and coupled Brusselators, and the Willamowski-Roessler system. Analytical results are confirmed convincingly in numerical simulations. The effect is quite general, and occurs whenever the Floquet multipliers governing the stability of the limit cycle are complex, with the amplitude of the oscillations increasing as the instability boundary is approached.
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