Baek, Hunki The dynamics of a predator-prey system with state-dependent feedback control. (English) Zbl 1243.34061 Abstr. Appl. Anal. 2012, Article ID 101386, 17 p. (2012). Summary: A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways. Using the Poincaré map and the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained. In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions. The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation. Numerical simulations to substantiate our theoretical results are provided. Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations. Cited in 4 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D25 Population dynamics (general) 93B52 Feedback control 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations Keywords:impulsive state feedback control PDFBibTeX XMLCite \textit{H. Baek}, Abstr. Appl. Anal. 2012, Article ID 101386, 17 p. (2012; Zbl 1243.34061) Full Text: DOI References: [1] M. G. Roberts and R. R. Kao, “The dynamics of an infectious disease in a population with birth pulses,” Mathematical Biosciences, vol. 149, no. 1, pp. 23-36, 1998. · Zbl 0928.92027 [2] S. Tang and L. 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