Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 53, Issue -, Pages 65-82Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2017.04.022
Keywords
Two-prey-one-predator model; Random perturbations; Delays; Stability in distribution
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Funding
- Natural Science Foundation of PR China [11301207]
- Chinese Postdoctoral Science Foundation [2015M571349, 2016T90236]
- 333 High-level Personnel Training Project
- Qing Lan Project of Jiangsu province
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This paper is concerned with the stability in distribution of a delay stochastic population model with two competing preys (X-1 and X-2) and one predator (X-3). Under some assumptions we prove that there are three numbers gamma(1) > gamma(2) > gamma(3) which have the following properties: if gamma(1) < 1, then all the populations go to extinction almost surely (a.s.), i.e., lim(t ->+infinity)X(i)(t) = 0 a.s., i = 1, 2,3; If gamma(i) > 1 > gamma(i+1) i = 1,2, then the distribution of (X-1(t),...,X-i(t))(T) converges weakly to a unique ergodic invariant distribution and lim(t ->+infinity)X(j)(t)= 0 a.s., j = i+1,...,3; If gamma(3) > 1, then the distribution of (X-1(t), X-2(t), X-3(t))(T) converges weakly to a unique ergodic invariant distribution a.s.. The influence of random perturbations on the stability are discussed and some numerical simulations are given to illustrate the main results. (C) 2017 Elsevier B.V. All rights reserved.
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