Existence, uniqueness and asymptotic stability of periodic solutions of periodic functional differential systems

Baorong Tang, Yang Kuang

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

We consider here a general Lotka-Volterra type n-dimensional periodic functional differential system. Sufficient conditions for the existence, uniqueness and global asymptotic stability of periodic solutions are established by combining the theory of monotone flow generated by FDEs, Horn's asymptotic fixed point theorem and linearized stability analysis. These conditions improve and generalize the recent ones obtained by Freedman and Wu (1992) for scalar equations. We also present a nontrivial application of our results to a delayed nonautonomous predator-prey system.

Original languageEnglish (US)
Pages (from-to)217-239
Number of pages23
JournalTohoku Mathematical Journal
Volume49
Issue number2
StatePublished - Jun 1997

Fingerprint

Lotka-Volterra
Nonautonomous Systems
Predator-prey System
Global Asymptotic Stability
Differential System
Asymptotic Stability
Fixed point theorem
n-dimensional
Stability Analysis
Monotone
Periodic Solution
Existence and Uniqueness
Scalar
Generalise
Sufficient Conditions

Keywords

  • Existence
  • Fixed point
  • Lotka-Volterra systems
  • Monotone theory
  • Periodic delay nonautonomous systems
  • Predator-prey systems
  • Uniform persistence
  • Uniqueness and globally asymptotic stability of periodic solutions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Existence, uniqueness and asymptotic stability of periodic solutions of periodic functional differential systems. / Tang, Baorong; Kuang, Yang.

In: Tohoku Mathematical Journal, Vol. 49, No. 2, 06.1997, p. 217-239.

Research output: Contribution to journalArticle

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