DYNAMICS OF A GENERAL NON-AUTONOMOUS STOCHASTIC LOTKA-VOLTERRA MODEL WITH DELAYS

Qing Wang; Yongguang Yu; Shuo Zhang

doi:10.11948/2016051

2016 Volume 6 Issue 3

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Qing Wang, Yongguang Yu, Shuo Zhang. DYNAMICS OF A GENERAL NON-AUTONOMOUS STOCHASTIC LOTKA-VOLTERRA MODEL WITH DELAYS[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 790-816. doi: 10.11948/2016051

Citation:

Qing Wang, Yongguang Yu, Shuo Zhang. DYNAMICS OF A GENERAL NON-AUTONOMOUS STOCHASTIC LOTKA-VOLTERRA MODEL WITH DELAYS[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 790-816. doi: 10.11948/2016051

DYNAMICS OF A GENERAL NON-AUTONOMOUS STOCHASTIC LOTKA-VOLTERRA MODEL WITH DELAYS

Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China

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Abstract

Abstract

In this paper, a general non-autonomous n-species Lotka-Volterra model with delays and stochastic perturbation is investigated. For this model, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The influences of the stochastic noises to the properties of the stochastic model are discussed. The property permanence for the model is preserved with the sufficiently small noise and sufficiently large noise may cause extinction of the model. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.
- Non-autonomous Lotka-Valterra model /
- stochastic perturbation /
- delays /
- persistence /
- extinction
MSC: 34F05;60H10

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