STOCHASTIC LOTKA-VOLTERRA SYSTEM

摘要

Generalized Lotka-Volterra LV model is considered, with the equation for preys reproduction containing quadratic term that accounts for interspecies competition and term with white-noise random variations of the preys reproduction factor which simulate the environmental variations. An exact solution is obtained for the corresponding Fokker-Planck-Kolmogorov equation for joint stationary probability density (p.d.f.) of the population sizes. Both population sizes are shown to be independent gamma-distributed stationary random processes. Increasing level of the environmental variations and/or approaching bifurcation point, which corresponds to extinction of predators, may lead to an intermittent behavior, whereby one or both population sizes experience very rare and violent short pulses or outbreaks while remaining on a very low level most of the time. This intermittency is described analytically in terms of the derived p.d.f. as well as by applying theory of excursions of random functions and by predicting p.d.f. of peaks and troughs in the predators population size.