Global stability in diffusive delay Lotka-Volterra systems

Y. Kuangt, Hal Smith, Klaus Schmitt

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We consider the global asymptotic stability of diffusive delay Latka-Volterra systems which may model population dynamics of closed ecological environments containing n interacting species. The first part of this paper deals with discrete delay case, where both continuous and discrete diffusion situations are considered. The second part of this paper studies unbounded continuous delay cases, where the integral kernels are assumed to satisfy linear differential equations with constant coefficients. In both parts, sufficient conditions for global asymptotic stability of the unique positive steady states are derived via some proper Lyapunov functions. To some extent, these results indicate that the diffusivity of the system may not affect the global asymptotic stability of its reaction system.

Original languageEnglish (US)
Pages (from-to)117-128
Number of pages12
JournalDifferential and Integral Equations
Volume4
Issue number1
StatePublished - 1991

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Lotka-Volterra System
Delay Systems
Global Asymptotic Stability
Asymptotic stability
Global Stability
Discrete Delay
Population dynamics
Lyapunov functions
Volterra
Diffusivity
Population Dynamics
Linear differential equation
Lyapunov Function
Differential equations
kernel
Closed
Sufficient Conditions
Coefficient
Model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Global stability in diffusive delay Lotka-Volterra systems. / Kuangt, Y.; Smith, Hal; Schmitt, Klaus.

In: Differential and Integral Equations, Vol. 4, No. 1, 1991, p. 117-128.

Research output: Contribution to journalArticle

Kuangt, Y. ; Smith, Hal ; Schmitt, Klaus. / Global stability in diffusive delay Lotka-Volterra systems. In: Differential and Integral Equations. 1991 ; Vol. 4, No. 1. pp. 117-128.
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