Research Article Open Access

Bifurcation and Controlling Chaos in a Discrete-Time Biological System

Guo Feng1
  • 1 Shandong Women’s University, Jinan, China

Abstract

The dynamics of a discrete-time food chain model with strong pressure on preys is investigated. The types of equilibria of the system are analyzed using stability theory and bifurcation theory. The route to chaos via Neimark-Sacker bifurcation followed by period-doubling bifurcations of invariant curves is found for some parameter values through numerical simulation. Moreover, the chaos is controlled on the stable periodic period-1 orbit by the improvement of OGY method. It is shown that the number of iterations used to control chaotic motion on a stable periodic orbit is difference, when the selected regulator poles are different. Numerical simulations are presented to illustrate our results based on the theoretical analysis and show the effect of the control method.

American Journal of Biochemistry and Biotechnology
Volume 16 No. 3, 2020, 299-307

DOI: https://doi.org/10.3844/ajbbsp.2020.299.307

Submitted On: 11 June 2020 Published On: 7 July 2020

How to Cite: Feng, G. (2020). Bifurcation and Controlling Chaos in a Discrete-Time Biological System. American Journal of Biochemistry and Biotechnology, 16(3), 299-307. https://doi.org/10.3844/ajbbsp.2020.299.307

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Keywords

  • Food Chain Model
  • Neimark-Sacker Bifurcation
  • Chaos Control
  • OGY Method