Stochastic dynamics in a nonautonomous prey-predator system with impulsive perturbations and Lévy jumps

Chao Liu; Ming Liu

doi:10.1016/j.cnsns.2019.104851

Stochastic dynamics in a nonautonomous prey-predator system with impulsive perturbations and Lévy jumps

Chao Liu^*
, Ming Liu

^*Corresponding author for this work

Northeastern University China
School of Astronautics, Harbin Institute of Technology

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

12 Scopus citations

Abstract

In this paper, a nonautonomous impulsive stochastic prey-predator system with modified Holling II functional response is established, where impulsive perturbations and Lévy jumps are taken into accounts. Combined dynamic effects of impulse phenomenon and stochastic disturbances on population dynamics are studied. Sufficient conditions for existence and uniqueness of globally attractive τ−periodic solution of the subsystem are investigated. Stochastically ultimate boundedness of the solution is discussed. Furthermore, some corresponding threshold values in the mean are derived to discuss stochastic persistence and extinction of the proposed system. Numerical simulations are supported to show consistency with theoretical analysis.

Original language	English
Article number	104851
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	78
DOIs	https://doi.org/10.1016/j.cnsns.2019.104851
State	Published - Nov 2019
Externally published	Yes

Keywords

Impulsive perturbations
Lévy jumps
Stochastic persistence
Stochastically ultimate boundedness

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10.1016/j.cnsns.2019.104851

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title = "Stochastic dynamics in a nonautonomous prey-predator system with impulsive perturbations and L{\'e}vy jumps",

abstract = "In this paper, a nonautonomous impulsive stochastic prey-predator system with modified Holling II functional response is established, where impulsive perturbations and L{\'e}vy jumps are taken into accounts. Combined dynamic effects of impulse phenomenon and stochastic disturbances on population dynamics are studied. Sufficient conditions for existence and uniqueness of globally attractive τ−periodic solution of the subsystem are investigated. Stochastically ultimate boundedness of the solution is discussed. Furthermore, some corresponding threshold values in the mean are derived to discuss stochastic persistence and extinction of the proposed system. Numerical simulations are supported to show consistency with theoretical analysis.",

keywords = "Impulsive perturbations, L{\'e}vy jumps, Stochastic persistence, Stochastically ultimate boundedness",

author = "Chao Liu and Ming Liu",

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

year = "2019",

month = nov,

doi = "10.1016/j.cnsns.2019.104851",

language = "英语",

volume = "78",

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TY - JOUR

T1 - Stochastic dynamics in a nonautonomous prey-predator system with impulsive perturbations and Lévy jumps

AU - Liu, Chao

AU - Liu, Ming

PY - 2019/11

Y1 - 2019/11

N2 - In this paper, a nonautonomous impulsive stochastic prey-predator system with modified Holling II functional response is established, where impulsive perturbations and Lévy jumps are taken into accounts. Combined dynamic effects of impulse phenomenon and stochastic disturbances on population dynamics are studied. Sufficient conditions for existence and uniqueness of globally attractive τ−periodic solution of the subsystem are investigated. Stochastically ultimate boundedness of the solution is discussed. Furthermore, some corresponding threshold values in the mean are derived to discuss stochastic persistence and extinction of the proposed system. Numerical simulations are supported to show consistency with theoretical analysis.

AB - In this paper, a nonautonomous impulsive stochastic prey-predator system with modified Holling II functional response is established, where impulsive perturbations and Lévy jumps are taken into accounts. Combined dynamic effects of impulse phenomenon and stochastic disturbances on population dynamics are studied. Sufficient conditions for existence and uniqueness of globally attractive τ−periodic solution of the subsystem are investigated. Stochastically ultimate boundedness of the solution is discussed. Furthermore, some corresponding threshold values in the mean are derived to discuss stochastic persistence and extinction of the proposed system. Numerical simulations are supported to show consistency with theoretical analysis.

KW - Impulsive perturbations

KW - Lévy jumps

KW - Stochastic persistence

KW - Stochastically ultimate boundedness

UR - https://www.scopus.com/pages/publications/85066141891

U2 - 10.1016/j.cnsns.2019.104851

DO - 10.1016/j.cnsns.2019.104851

M3 - 文章

AN - SCOPUS:85066141891

SN - 1007-5704

VL - 78

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 104851

ER -

Stochastic dynamics in a nonautonomous prey-predator system with impulsive perturbations and Lévy jumps

Abstract

Keywords

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