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The discrete Rosenzweig model. (English) Zbl 0694.92014
Summary: Discrete time versions of the Rosenzweig predator-prey model [see {\it M. L. Rosenzweig}, Science 171, 385-387 (1971)] are studied by analytic and numerical methods. The interaction of the Hopf bifurcation leading to periodic orbits and the period-doubling bifurcation are investigated. It is shown that for certain choices of the parameters there is stable coexistence of both species together with a local attractor at which the prey is absent.

MSC:
92D25Population dynamics (general)
39A12Discrete version of topics in analysis
39A11Stability of difference equations (MSC2000)
65C20Models (numerical methods)
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