Dynamical behavior of stochastic delay Lotka–Volterra competitive model with general Lévy jumps

Chun Lu; Xiaohua Ding

doi:10.1016/j.physa.2019.121730

Dynamical behavior of stochastic delay Lotka–Volterra competitive model with general Lévy jumps

Chun Lu^*
, Xiaohua Ding

^*Corresponding author for this work

Qingdao University of Technology
Harbin Institute of Technology Weihai

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

15 Scopus citations

Abstract

This paper considers a stochastic competitive model with infinite delay and general Lévy jumps. Sufficient conditions for stability in time average are established as well as permanence in time average and extinction. The easily verifiable sufficient criteria for the existence of stability in distribution are established. Our results reveal that, firstly, stability in time average, permanence in time average and extinction have close relationships with general Lévy jumps; secondly, based on a simple assumption, infinite delays are disadvantageous to permanence in time average and stability in distribution. Finally, numerical simulations are introduced to support the theoretical analysis results.

Original language	English
Article number	121730
Journal	Physica A: Statistical Mechanics and its Applications
Volume	531
DOIs	https://doi.org/10.1016/j.physa.2019.121730
State	Published - 1 Oct 2019
Externally published	Yes

Keywords

General Lévy jumps
Infinite delay
Lotka–Volterra competitive model
Permanence in time average
Stability in distribution

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10.1016/j.physa.2019.121730

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title = "Dynamical behavior of stochastic delay Lotka–Volterra competitive model with general L{\'e}vy jumps",

abstract = "This paper considers a stochastic competitive model with infinite delay and general L{\'e}vy jumps. Sufficient conditions for stability in time average are established as well as permanence in time average and extinction. The easily verifiable sufficient criteria for the existence of stability in distribution are established. Our results reveal that, firstly, stability in time average, permanence in time average and extinction have close relationships with general L{\'e}vy jumps; secondly, based on a simple assumption, infinite delays are disadvantageous to permanence in time average and stability in distribution. Finally, numerical simulations are introduced to support the theoretical analysis results.",

keywords = "General L{\'e}vy jumps, Infinite delay, Lotka–Volterra competitive model, Permanence in time average, Stability in distribution",

author = "Chun Lu and Xiaohua Ding",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = oct,

day = "1",

doi = "10.1016/j.physa.2019.121730",

language = "英语",

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journal = "Physica A: Statistical Mechanics and its Applications",

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TY - JOUR

T1 - Dynamical behavior of stochastic delay Lotka–Volterra competitive model with general Lévy jumps

AU - Lu, Chun

AU - Ding, Xiaohua

PY - 2019/10/1

Y1 - 2019/10/1

N2 - This paper considers a stochastic competitive model with infinite delay and general Lévy jumps. Sufficient conditions for stability in time average are established as well as permanence in time average and extinction. The easily verifiable sufficient criteria for the existence of stability in distribution are established. Our results reveal that, firstly, stability in time average, permanence in time average and extinction have close relationships with general Lévy jumps; secondly, based on a simple assumption, infinite delays are disadvantageous to permanence in time average and stability in distribution. Finally, numerical simulations are introduced to support the theoretical analysis results.

AB - This paper considers a stochastic competitive model with infinite delay and general Lévy jumps. Sufficient conditions for stability in time average are established as well as permanence in time average and extinction. The easily verifiable sufficient criteria for the existence of stability in distribution are established. Our results reveal that, firstly, stability in time average, permanence in time average and extinction have close relationships with general Lévy jumps; secondly, based on a simple assumption, infinite delays are disadvantageous to permanence in time average and stability in distribution. Finally, numerical simulations are introduced to support the theoretical analysis results.

KW - General Lévy jumps

KW - Infinite delay

KW - Lotka–Volterra competitive model

KW - Permanence in time average

KW - Stability in distribution

UR - https://www.scopus.com/pages/publications/85067032439

U2 - 10.1016/j.physa.2019.121730

DO - 10.1016/j.physa.2019.121730

M3 - 文章

AN - SCOPUS:85067032439

SN - 0378-4371

VL - 531

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 121730

ER -

Dynamical behavior of stochastic delay Lotka–Volterra competitive model with general Lévy jumps

Abstract

Keywords

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