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

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Kartal S., Gurcan F.

JOURNAL OF BIOLOGICAL DYNAMICS, cilt.9, sa.1, ss.159-171, 2015 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1080/17513758.2015.1049225
  • Dergi Adı: JOURNAL OF BIOLOGICAL DYNAMICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.159-171
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.