Stochastic mutualism model with Lévy jumps

Qun Liu; Daqing Jiang; Ningzhong Shi; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.cnsns.2016.05.003

Stochastic mutualism model with Lévy jumps

Qun Liu
, Daqing Jiang
, Ningzhong Shi
, Tasawar Hayat
, Ahmed Alsaedi

Northeast Normal University
Yulin Normal University
Faculty of Sciences, King Abdulaziz University
China University of Petroleum (East China)
Quaid-I-Azam University

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

51 Scopus citations

Abstract

In this paper, we consider a stochastic mutualism model with Lévy jumps. First of all, we show that the positive solution of the system is stochastically ultimate bounded. Then under a simple assumption, we establish sufficient and necessary conditions for the stochastic permanence and extinction of the system. The results show an important property of the Lévy jumps: they are unfavorable for the permanence of the species. Moreover, when there are no Lévy jumps, we show that there is a unique ergodic stationary distribution of the corresponding system under certain conditions. Some numerical simulations are introduced to validate the theoretical results.

Original language	English
Pages (from-to)	78-90
Number of pages	13
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	43
DOIs	https://doi.org/10.1016/j.cnsns.2016.05.003
State	Published - 1 Feb 2017
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 15 Life on Land

Keywords

Lévy jumps
Mutualism model
Stochastic permanence and extinction
Stochastically ultimate boundedness

Access to Document

10.1016/j.cnsns.2016.05.003

Cite this

@article{6e3b0cc840a84506a18d7d31f7ceb7f0,

title = "Stochastic mutualism model with L{\'e}vy jumps",

abstract = "In this paper, we consider a stochastic mutualism model with L{\'e}vy jumps. First of all, we show that the positive solution of the system is stochastically ultimate bounded. Then under a simple assumption, we establish sufficient and necessary conditions for the stochastic permanence and extinction of the system. The results show an important property of the L{\'e}vy jumps: they are unfavorable for the permanence of the species. Moreover, when there are no L{\'e}vy jumps, we show that there is a unique ergodic stationary distribution of the corresponding system under certain conditions. Some numerical simulations are introduced to validate the theoretical results.",

keywords = "L{\'e}vy jumps, Mutualism model, Stochastic permanence and extinction, Stochastically ultimate boundedness",

author = "Qun Liu and Daqing Jiang and Ningzhong Shi and Tasawar Hayat and Ahmed Alsaedi",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

month = feb,

day = "1",

doi = "10.1016/j.cnsns.2016.05.003",

language = "English",

volume = "43",

pages = "78--90",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Stochastic mutualism model with Lévy jumps

AU - Liu, Qun

AU - Jiang, Daqing

AU - Shi, Ningzhong

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2017/2/1

Y1 - 2017/2/1

N2 - In this paper, we consider a stochastic mutualism model with Lévy jumps. First of all, we show that the positive solution of the system is stochastically ultimate bounded. Then under a simple assumption, we establish sufficient and necessary conditions for the stochastic permanence and extinction of the system. The results show an important property of the Lévy jumps: they are unfavorable for the permanence of the species. Moreover, when there are no Lévy jumps, we show that there is a unique ergodic stationary distribution of the corresponding system under certain conditions. Some numerical simulations are introduced to validate the theoretical results.

AB - In this paper, we consider a stochastic mutualism model with Lévy jumps. First of all, we show that the positive solution of the system is stochastically ultimate bounded. Then under a simple assumption, we establish sufficient and necessary conditions for the stochastic permanence and extinction of the system. The results show an important property of the Lévy jumps: they are unfavorable for the permanence of the species. Moreover, when there are no Lévy jumps, we show that there is a unique ergodic stationary distribution of the corresponding system under certain conditions. Some numerical simulations are introduced to validate the theoretical results.

KW - Lévy jumps

KW - Mutualism model

KW - Stochastic permanence and extinction

KW - Stochastically ultimate boundedness

UR - https://www.scopus.com/pages/publications/84976447826

U2 - 10.1016/j.cnsns.2016.05.003

DO - 10.1016/j.cnsns.2016.05.003

M3 - Article

AN - SCOPUS:84976447826

SN - 1007-5704

VL - 43

SP - 78

EP - 90

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

Stochastic mutualism model with Lévy jumps

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this