TY - JOUR AU - Zhao, Ming AU - Xuan, Zuxing AU - Li, Cuiping PY - 2016 DA - 2016/07/13 TI - Dynamics of a discrete-time predator-prey system JO - Advances in Difference Equations SP - 191 VL - 2016 IS - 1 AB - We investigate the dynamics of a discrete-time predator-prey system. Firstly, we give necessary and sufficient conditions of the existence and stability of the fixed points. Secondly, we show that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation by using center manifold theorem and bifurcation theory. Furthermore, we present numerical simulations not only to show the consistence with our theoretical analysis, but also to exhibit the complex but interesting dynamical behaviors, such as the period-6, -11, -16, -18, -20, -21, -24, -27, and -37 orbits, attracting invariant cycles, quasi-periodic orbits, nice chaotic behaviors, which appear and disappear suddenly, coexisting chaotic attractors, etc. These results reveal far richer dynamics of the discrete-time predator-prey system. Finally, we have stabilized the chaotic orbits at an unstable fixed point using the feedback control method. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-016-0903-6 DO - 10.1186/s13662-016-0903-6 ID - Zhao2016 ER -