Limit cycles, complex Floquet multipliers, and intrinsic noise
Limit cycles, complex Floquet multipliers, and intrinsic noise
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DOI：
10.1103/physreve.79.051131
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发表时间：
2009-05-01
影响因子：
2.4
通讯作者：
McKane, Alan J.
中科院分区：
文献类型：
--
作者：
Boland, Richard P.;Galla, Tobias;McKane, Alan J.
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。我们计算的相关函数和光谱特性的波动在适当的共动Frenet框架的几个模型系统，包括驱动和耦合的双折射系统，和Willamowski-Rossler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。
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 comoving Frenet frames for several model systems including driven and coupled Brusselators, and the Willamowski-Rossler 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.