Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

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Kangalgil F., Işık S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.5, pp.1761-1776, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.531024
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1761-1776
  • Keywords: predator-prey model, fixed point, stability, Neimark-Sacker bifurcation, chaotic behavior, OGY feedback control method, FUNCTIONAL-RESPONSE, MODEL, STABILITY, BEHAVIOR
  • Dokuz Eylül University Affiliated: Yes

Abstract

This article is about a discrete-time predator-prey model obtained by the forward Euler method. The stability of the fixed point of the model and the existence conditions of the Neimark-Sacker bifurcation are investigated. In addition, the direction of the Neimark-Sacker bifurcation is given. Moreover, OGY control method is to implement to control chaos caused by the Neimark-Sacker bifurcation. Finally, Neimark-Sacker bifurcation, chaos control strategy, and asymptotic stability of the only positive fixed point are verified with the help of numerical simulations. The existence of chaotic behavior in the model is confirmed by computing of the maximum Lyapunov exponents.