Global Stability of N-Dimensional Nonautonomous Lotka-Volterra System

Xue Zhong He

doi:10.1080/00036819308840196

Global Stability of N-Dimensional Nonautonomous Lotka-Volterra System

Xue Zhong He^*

^*Corresponding author for this work

Flinders University

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

Abstract

In this paper, we deal with the global asymptotic stability of n-dimensional Lotka-Volterra system with time dependent coefficients. By constructing suitable Lyapunov functions, we generalize Theorems 3.1 and 3.2 of [6] to our n-dimensional case and therefore have solved the open problem given in [6]. We also discuss the global stability of the periodic solution of the system when all the coefficients of the system are periodic. For the case of n = 2, we have improved the corresponding results in [6].

Original language	English
Pages (from-to)	253-262
Number of pages	10
Journal	Applicable Analysis
Volume	50
Issue number	3-4
DOIs	https://doi.org/10.1080/00036819308840196
Publication status	Published - 1 Sept 1993
Externally published	Yes

Keywords

Lyapunov functions
global stability
periodic solution

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10.1080/00036819308840196

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title = "Global Stability of N-Dimensional Nonautonomous Lotka-Volterra System",

abstract = "In this paper, we deal with the global asymptotic stability of n-dimensional Lotka-Volterra system with time dependent coefficients. By constructing suitable Lyapunov functions, we generalize Theorems 3.1 and 3.2 of [6] to our n-dimensional case and therefore have solved the open problem given in [6]. We also discuss the global stability of the periodic solution of the system when all the coefficients of the system are periodic. For the case of n = 2, we have improved the corresponding results in [6].",

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AB - In this paper, we deal with the global asymptotic stability of n-dimensional Lotka-Volterra system with time dependent coefficients. By constructing suitable Lyapunov functions, we generalize Theorems 3.1 and 3.2 of [6] to our n-dimensional case and therefore have solved the open problem given in [6]. We also discuss the global stability of the periodic solution of the system when all the coefficients of the system are periodic. For the case of n = 2, we have improved the corresponding results in [6].

KW - Lyapunov functions

KW - global stability

KW - periodic solution

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Global Stability of N-Dimensional Nonautonomous Lotka-Volterra System

Abstract

Keywords

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