Stability of a delayed predator–prey model in a random environment

doi:10.1088/1674-1056/24/11/110501

Abstract

The stability of the first-order and second-order solution moments for a Harrison-type predator-prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Itô interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.

Keywords: delay-independent stability predator-prey model moment equations environmental noise

Received: 15 April 2015
Revised: 06 June 2015
Accepted manuscript online:

PACS:	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	02.50.-r	(Probability theory, stochastic processes, and statistics)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11272051 and 11302172).

Corresponding Authors: Jin Yan-Fei
E-mail: jinyf@bit.edu.cn

Cite this article:

Jin Yan-Fei (靳艳飞), Xie Wen-Xian (谢文贤) Stability of a delayed predator–prey model in a random environment 2015 Chin. Phys. B 24 110501

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