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Journal of Applied Mathematics and Computing

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20-05-2017 | Original Research

Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations

Authors: Chun Lu, Jian Chen, Xingkui Fan, Lei Zhang

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2018

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Abstract

This paper considers a stochastic predator-prey model with infinite delay and impulsive perturbations. Sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of the stochasic model. Some simulation figures, which are obtained by the split-step \(\theta \)-method to discretize the stochasic model, are introduced to support the analytical findings. Our results demonstrate that, firstly, impulsive perturbations which may represent human factor play a key role in maintaining ecological balance; secondly, environmental noise, which can be modelled by Brownian motion, is disadvantageous to population survival; finally, infinite delay has not affect permanence in time average, extinction, stability in time average and global attractivity of the stochasic model.

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Title: Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations
Authors: Chun Lu
Jian Chen
Xingkui Fan
Lei Zhang
Publication date: 20-05-2017
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2018
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-017-1114-3

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