Numerical integration of a stochastic model for the Volterra-Lotka reaction

Abstract

Time-integration of the master equation governing the birth-and-death model of the Volterra-Lotka reaction is carried out for three different initial conditions, with the results: (i) Fluctuations destroy the deterministic steady state in a manner quantitatively predicted from a cumulant expansion; (ii) The sustained oscillatory behavior predicted by the deterministic model degenerated after 1/4 cycle in the stochastic model; (iii) It is possible to select initial distributions such that the asymptotic distribution is a spike at the origin of the plane of reactants. © 1976 Society for Mathematical Biology.