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Bifurcations and chaos control in a discrete-time predator-prey system of Leslie type
Sarker Md. Sohel Rana
Keywords:discrete-time predator-prey system; bifurcations; chaos; Lyapunov exponents; feedback control
Abstract:
      The population models in ecology and mathematical ecology which describe predator-prey interaction geverned by differential equations studied extensively by many researchers \cite{hsuW, HuangRS} and the reference therein. Qualitative analyses of these works found many rich dynamics which include global stability, stable limit cycle, bifurcatioins and persistence analysis. But in recent years, there is a growing evidence that the discretization of predator-prey models governed by difference equations are more appropriate than the continuous ones, especially when the populations have non-overlapping generations \cite{hebo, he, huC, rana3, rana1, tan, wang, zhaoX, zhao}. The main studied subjects in discrete-time models were the posibility of bifurcations and chaos phenomenon those had been performed either by using numerical simulations or by using the center manifold theorem and bifurcation theory.