Stability of a time-varying fishing model with delay

L. Berezansky, L. Idels

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

To incorporate ecosystem effects, environmental variability and other factors that affect the population growth, the periodicity of the parameters of the model is assumed. We introduce a delay differential equation model which describes how fish are harvested: (A)over(N, ̇) (t) = [frac(a (t), 1 + (frac(N (θ (t)), K (t)))γ) - b (t)] N (t) . In our previous studies the persistence of Eq. (A) and the existence of a periodic solution to this equation were investigated. In the present paper the explicit conditions of global attractivity of the positive periodic solutions to Eq. (A) are obtained. It will also be shown that if the stability conditions are violated, the model exhibits sustained oscillations.

Original languageEnglish
Pages (from-to)447-452
Number of pages6
JournalApplied Mathematics Letters
Volume21
Issue number5
DOIs
StatePublished - 1 May 2008

Keywords

  • Delay differential equations
  • Fishery
  • Global and local stability
  • Periodic environment

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