Stochastic Transients of Noisy Lotka-Volterra Model

梁鍹廣(H. K. Leung)

《Chinese Journal of Physics》 29卷6期 (1991/12) Pp. 637-652

並列摘要

A Lotka-Volterra model system perturbed by external noises is investigated in detail. Spatial homogeneity is assumed over the reacting system. External white noises are realized either as additional random forces in rate equations, or as rapid fluctuating parts of various rate parameters. Transient properties are described in terms of the average concentrations together with the fluctuations and correlation among them. The system which is marginally stable in deterministic theory, turns out to be unstable due to noises. Fluctuations are found to be increasing with noise intensities. For a given value of noise intensity, fluctuations are oscillating and incresing monotonically with time. The closed phase trajectories are found to be spiraling toward absorbing boundaries. Approximate period can be determined numerically to demonstrate the noise-induced slowing-down phenomenon. It is found that period always increases with noise intensity, and that successive cycles take longer and longer period. Due to fluctuations, a Lyapunov function of the system is found to be more positive and oscillating with time. The time rate of change of this function is derived analytically, and is found to have distinct contributions from the intrinsic and extrinsic stochasticities.