STATIONARY DISTRIBUTION AND PERMANENCE OF A STOCHASTIC DELAY PREDATOR-PREY LOTKA-VOLTERRA MODEL WITH LÉVY JUMPS

Chun Lu; Xiaohua Ding; Lei Zhang

doi:10.11948/20210077

STATIONARY DISTRIBUTION AND PERMANENCE OF A STOCHASTIC DELAY PREDATOR-PREY LOTKA-VOLTERRA MODEL WITH LÉVY JUMPS

Chun Lu^*
, Xiaohua Ding
, Lei Zhang

^*Corresponding author for this work

Qingdao University of Technology
Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we propose and investigate an impulsive stochastic predator-prey Lotka-Volterra model with infinite delay and Lévy jumps. Sufficient criteria for permanence in time average and the threshold between stability in time average and extinction are provided. For the corresponding case without impulse, the easily substantiated sufficient criteria for stability in distribution are derived. Our results demonstrate that, first of all, the coeffi-cients related to infinite delay have some effects on permanence in time average and stability in distribution; then impulsive perturbations play a prominent part in keeping the permanence in time average despite the unfavourable factor Lévy jumps causes.

Original language	English
Pages (from-to)	1328-1352
Number of pages	25
Journal	Journal of Applied Analysis and Computation
Volume	12
Issue number	4
DOIs	https://doi.org/10.11948/20210077
State	Published - 2022
Externally published	Yes

Keywords

Lévy jumps
Predator-prey Lotka-Volterra model
impulsive perturba-tions
infinite delay
permanence in time aver-age
stability in distribution

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title = "STATIONARY DISTRIBUTION AND PERMANENCE OF A STOCHASTIC DELAY PREDATOR-PREY LOTKA-VOLTERRA MODEL WITH L{\'E}VY JUMPS",

abstract = "In this paper, we propose and investigate an impulsive stochastic predator-prey Lotka-Volterra model with infinite delay and L{\'e}vy jumps. Sufficient criteria for permanence in time average and the threshold between stability in time average and extinction are provided. For the corresponding case without impulse, the easily substantiated sufficient criteria for stability in distribution are derived. Our results demonstrate that, first of all, the coeffi-cients related to infinite delay have some effects on permanence in time average and stability in distribution; then impulsive perturbations play a prominent part in keeping the permanence in time average despite the unfavourable factor L{\'e}vy jumps causes.",

keywords = "L{\'e}vy jumps, Predator-prey Lotka-Volterra model, impulsive perturba-tions, infinite delay, permanence in time aver-age, stability in distribution",

author = "Chun Lu and Xiaohua Ding and Lei Zhang",

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AU - Lu, Chun

AU - Ding, Xiaohua

AU - Zhang, Lei

PY - 2022

Y1 - 2022

N2 - In this paper, we propose and investigate an impulsive stochastic predator-prey Lotka-Volterra model with infinite delay and Lévy jumps. Sufficient criteria for permanence in time average and the threshold between stability in time average and extinction are provided. For the corresponding case without impulse, the easily substantiated sufficient criteria for stability in distribution are derived. Our results demonstrate that, first of all, the coeffi-cients related to infinite delay have some effects on permanence in time average and stability in distribution; then impulsive perturbations play a prominent part in keeping the permanence in time average despite the unfavourable factor Lévy jumps causes.

AB - In this paper, we propose and investigate an impulsive stochastic predator-prey Lotka-Volterra model with infinite delay and Lévy jumps. Sufficient criteria for permanence in time average and the threshold between stability in time average and extinction are provided. For the corresponding case without impulse, the easily substantiated sufficient criteria for stability in distribution are derived. Our results demonstrate that, first of all, the coeffi-cients related to infinite delay have some effects on permanence in time average and stability in distribution; then impulsive perturbations play a prominent part in keeping the permanence in time average despite the unfavourable factor Lévy jumps causes.

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KW - permanence in time aver-age

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STATIONARY DISTRIBUTION AND PERMANENCE OF A STOCHASTIC DELAY PREDATOR-PREY LOTKA-VOLTERRA MODEL WITH LÉVY JUMPS

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