Bifurcation and Controlling Chaos in a Discrete-Time Biological System
- 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.
DOI: https://doi.org/10.3844/ajbbsp.2020.299.307
Copyright: © 2020 Guo Feng. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Food Chain Model
- Neimark-Sacker Bifurcation
- Chaos Control
- OGY Method