On β-extinction and Stability of a Stochastic Lotka-Volterra System with Infinite Delay

被引：1

作者：

Zhao, Shu-fen ^{[1
]}

机构：

[1] Taishan Univ, Sch Math & Stat, Tai An 271000, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2024年 / 40卷 / 04期

关键词：

almost sure beta-extinction; Lotka-Volterra system; infinite delay; FUNCTIONAL-DIFFERENTIAL EQUATIONS; GLOBAL ASYMPTOTIC STABILITY; MODEL; TIME;

D O I：

10.1007/s10255-024-1078-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a stochastic Lotka-Volterra system with infinite delay is considered. A new concept of extinction, namely, the almost sure beta-extinction is proposed and sufficient conditions for the solution to be almost sure beta-extinction are obtained. When the positive equilibrium exists and the intensities of the noises are small enough, any solution of the system is attracted by the positive equilibrium. Finally, numerical simulations are carried out to support the results.

引用

页码：1045 / 1059

页数：15

共 28 条

[1] HARVESTING NATURAL-POPULATIONS IN A RANDOMLY FLUCTUATING ENVIRONMENT [J].

BEDDINGTON, JR ;

MAY, RM .

SCIENCE, 1977, 197 (4302) :463-465

[2] Ito versus Stratonovich calculus in random population growth [J].

Braumann, Carlos A. .

MATHEMATICAL BIOSCIENCES, 2007, 206 (01) :81-107

[3] Stability and Extinction for Lotka-Volterra Systems with Infinite Delay [J].

Faria, Teresa .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2010, 22 (02) :299-324

[4] GLOBAL ASYMPTOTIC STABILITY IN VOLTERRA POPULATION SYSTEMS [J].

GOPALSAMY, K .

JOURNAL OF MATHEMATICAL BIOLOGY, 1984, 19 (02) :157-168

[5] ON DENSITY AND EXTINCTION IN CONTINUOUS POPULATION-MODELS [J].

HALLAM, TG ;

MA, ZE .

JOURNAL OF MATHEMATICAL BIOLOGY, 1987, 25 (02) :191-201

[6]

Ikeda N, 1989, Stochastic differential equations and diffusion processes

[7] Ergodic stationary distribution and extinction of a n-species Gilpin-Ayala competition system with nonlinear random perturbations [J].

Jiang, Daqing ;

Zhou, Baoquan ;

Han, Bingtao .

APPLIED MATHEMATICS LETTERS, 2021, 120

[8] Analysis of autonomous Lotka-Volterra competition systems with random perturbation [J].

Jiang, Daqing ;

Ji, Chunyan ;

Li, Xiaoyue ;

O'Regan, Donal .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 390 (02) :582-595

[9]

Khasminski R., 1969, Stability of Systems of Differential Equations in the presence of Random Disturbances

[10]

LIU HP, 1991, J MATH BIOL, V30, P49, DOI 10.1007/BF00168006

← 1 2 3 →