All Issues

Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Bifurcations and chaos control in a discrete-time predator-prey system of Leslie type
Keywords:discrete-time predator-prey system; bifurcations; chaos; Lyapunov exponents; feedback control
      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.