Bifurcation and control of a predator-prey system with unfixed functional responses

<p style='text-indent:20px;'>In this paper we investigate a discrete-time predator-prey system with not only some constant parameters but also unfixed functional responses including growth rate function of prey, conversion factor and predation probability function. We prove that the maximal number fixed points is <inline-formula><tex-math id="M1">\begin{document}$ 3 $\end{document}</tex-math></inline-formula> give necessary sufficient conditions exactly id="M2">\begin{document}$ j $\end{document}</tex-math></inline-formula>(<inline-formula><tex-math id="M3">\begin{document}$ = 1,2,3 $\end{document}</tex-math></inline-formula>) points, respectively. For transcritical bifurcation Neimark-Sacker bifurcation, provide depending on these responses. In order to regulate stability biological system, hybrid control strategy used bifurcation. Finally, apply our main results examples carry out numerical simulations for each example verify correctness theoretical analysis.</p>