Oscillations and Convergence in an Almost Periodic Competition System

K. Gopalsamy*, Xue Zhong He

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

Sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a competition system modelled by the nonautonomous Lotka-Volterra delay differential equations dN1(t)/dt = N1(t)[r1(t)-a11(t)N1(t - τ(t)) - a12(t)N2(t - τ(t))], dN2(t)/dt = N2(t)[r2(t) - a21(t)N1(t - τ(t)) - a22(t)N2(t - τ(t))], in which τ, ri, aij (i, j = 1, 2) are continuous positive almost periodic functions; conditions are also obtained for all positive solutions of the above system to 'oscillate' about the unique almost periodic solution. Some ecobiological consequences of the convergence to almost periodicity and delay induced oscillations are briefly discussed.

Original languageEnglish
Pages (from-to)247-266
Number of pages20
JournalActa Applicandae Mathematicae
Volume46
Issue number3
DOIs
Publication statusPublished - 1997
Externally publishedYes

Keywords

  • Almost periodicity
  • Competition
  • Oscillations

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