Limit cycles, complex Floquet multipliers, and intrinsic noise

作者：Boland Richard P^*; Galla Tobias; McKane Alan J

来源：Physical Review E, 2009, 79(5): 051131.

DOI：10.1103/PhysRevE.79.051131

• differential equations
• limit cycles
• nonlinear dynamical systems
• oscillations
• random noise
• reaction kinetics theory

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.

• 出版日期2009-5