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Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response. (English) Zbl 1372.37134
Summary: A discrete predator-prey system with square root functional response is presented. We study the existence and local stability analysis of the system. The conditions of existence of flip and Niemark-Sacker bifurcations in the system are derived. Furthermore, the chaotic behavior of the system in the sense of Marotto is proved. Numerical simulations are performed to show the consistence with analytical results and also to exhibit the complexity of the system. Finally, chaos control in the system is achieved via OGY feedback control method.

MSC:
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
39A12 Discrete version of topics in analysis
39A30 Stability theory for difference equations
39A28 Bifurcation theory for difference equations
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