Eur. Phys. J. B 72, 607-618 (2009)
https://doi.org/10.1140/epjb/e2009-00388-7

The effects of time delay on the decline and propagation processes of population in the Malthus-Verhulst model with cross-correlated noises

Department of Physics, Yunnan University, Kunming, 650091, P.R. China

Corresponding author: ^a meidch@ynu.edu.cn

Received: 26 August 2009
Revised: 9 October 2009
Published online: 20 November 2009

Abstract

The effects of time delay on the decline and propagation processes of population in the Malthus-Verhulst model with cross-correlated noises are investigated separately. Through numerically computing and stochastically simulating, we find that: (i) inclusion of time delay in the decline process, increasing the delay time τ weakens the stability of population with short delay and strengthens it with long delay. The stability of population reduces monotonically as the cross-correlated intensity λ increasing. The population of a species goes to extinction with increasing τ and increasing λ; (ii) inclusion of time delay in the propagation process, the increasing τ strengthens the stability of population and the increasing λ weakens it. The increasing τ slows down the growth process of a species while the increasing λ speeds it up. That is, the increasing delay time does not affect roughly the stability of population with short delay but strengthens it with long delay, and the population of species is restricted in the lower level by the larger delay time. The stability of population is weakened and the replacement of old individuals with young ones is accelerated by the increasing cross-correlation intensity between two noises.