He, Zhimin; Lai, Xin Bifurcation and chaotic behavior of a discrete-time predator-prey system. (English) Zbl 1202.93038 Nonlinear Anal., Real World Appl. 12, No. 1, 403-417 (2011). Summary: The dynamics of a discrete-time predator-prey system is investigated in the closed first quadrant \(\mathbb R^2_+\). It is shown that the system undergoes flip bifurcation and Neimark-Sacker bifurcation in the interior of \(\mathbb R^2_+\) by using a center manifold theorem and bifurcation theory. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as orbits of period 7, 14, 21, 63, 70, cascades of period-doubling bifurcation in orbits of period 2, 4, 8, quasi-periodic orbits and chaotic sets. These results show far richer dynamics of the discrete model compared with the continuous model. Specifically, we have stabilized the chaotic orbits at an unstable fixed point using the feedback control method. Cited in 96 Documents MSC: 93B52 Feedback control 34H20 Bifurcation control of ordinary differential equations 49N75 Pursuit and evasion games Keywords:predator-prey system; chaos; discrete dynamical system; stability; flip bifurcation; period-doubling bifurcation; Neimark-Sacker bifurcation; feedback control PDFBibTeX XMLCite \textit{Z. He} and \textit{X. Lai}, Nonlinear Anal., Real World Appl. 12, No. 1, 403--417 (2011; Zbl 1202.93038) Full Text: DOI References: [1] Lotka, A. J., Elements of Mathematical Biology (1956), Dover: Dover New York · Zbl 0074.14404 [2] Volterra, V., Opere Matematiche, Memorie e Note, vol. V (1962), Acc. Naz. dei Lincei: Acc. Naz. dei Lincei Rome, Cremona · Zbl 0099.00102 [3] Holling, C. S., The functional response of predator to prey density and its role in mimicry and population regulation, Mem. Entomol. Soc. 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