Noise and time delay: Suppressed population explosion of the mutualism system

Abstract

We have analyzed effects of noise and time delay in a classical Lotka-Volterra model of mutualism system. We show that the consideration of the noise and the time delay change drastically the behavior of the system in the deterministic case. To a certain degree, the noise or the time delay can suppress the population explosion of the mutualism system, which takes place in the deterministic case, however, the average species population of system with only the noise or the time delay does not converge. Combination of the noise and the time delay completely suppress the population explosion of the mutualism system.