ANALYSIS OF AUTONOMOUS LOTKA-VOLTERRA SYSTEMS BY LÉVY NOISE

Qiumei Zhang; Daqing Jiang

doi:10.11948/20190212

2021 Volume 11 Issue 1

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Qiumei Zhang, Daqing Jiang. ANALYSIS OF AUTONOMOUS LOTKA-VOLTERRA SYSTEMS BY LÉVY NOISE[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 176-191. doi: 10.11948/20190212

Citation:

Qiumei Zhang, Daqing Jiang. ANALYSIS OF AUTONOMOUS LOTKA-VOLTERRA SYSTEMS BY LÉVY NOISE[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 176-191. doi: 10.11948/20190212

ANALYSIS OF AUTONOMOUS LOTKA-VOLTERRA SYSTEMS BY LÉVY NOISE

Qiumei Zhang^1,2,3,
Daqing Jiang^4,5, ,

1.
College of Mathematic, Jilin University, Changchun 130012, China
2.
School of Science, Changchun University, Changchun 130022, China
3.
Jilin Provincial Key Laboratory of Human Health Status Identification and Function Enhancement (Changchun University), Changchun 130022, China
4.
College of Science, China University of Petroleum(East China), Qingdao 266580, China
5.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Corresponding author: Email address: daqingjiang2010@hotmail.com(D.Jiang)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 11801040, 11871473), China Postdoctoral Science Foundation (No. 2018M631861) and Team Project of Jilin Provincial Department of Science and Technology (No. 20200301036RQ)

Abstract

Abstract

The present paper deals with the problem of autonomous LotkaVolterra systems by L´evy noise. The essential mathematical features are analyzed with the help of the existence and uniqueness of the positive solution, the pth moment boundedness, asymptotic pathwise estimation, extinction, asymptotic stability and persistence by Lyapunov analysis methods. An example of three species predator-prey chain model is presented to illustrate the analytical findings.
- Lévy noise /
- extinction /
- asymptotic stability /
- persistence
MSC: 60J05, 60J60, 93D05

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