Global behaviour of a predator-prey like model with piecewise constant arguments

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Kartal S., Gurcan F.

JOURNAL OF BIOLOGICAL DYNAMICS, vol.9, no.1, pp.159-171, 2015 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1080/17513758.2015.1049225
  • Journal Name: JOURNAL OF BIOLOGICAL DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.159-171
  • Erciyes University Affiliated: Yes

Abstract

The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle.