标题： 极限环，复 Floquet 乘子和内在噪声 显示英文标题

标题： Limit cycles, complex Floquet multipliers and intrinsic noise

摘要： 我们研究内在噪声对化学反应系统的影响，在确定性极限下系统以振荡方式接近极限环。 先前对以振荡方式接近固定点的系统的研究表明，噪声可以将振荡衰减转化为具有大振幅的持续相干振荡。 我们证明当稳定的吸引子是极限环时，会发生类似的效果。 我们计算了适用于几种模型系统的适当共动Frenet框架中的涨落相关函数和光谱特性，包括驱动和耦合的Brusselators，以及Willamowski-Roessler系统。 分析结果在数值模拟中得到了令人信服的验证。 这种效应非常普遍，只要控制极限环稳定性的Floquet乘数是复数，并且振荡幅度随着不稳定边界接近而增加时就会发生。 显示英文摘要

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.