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Bifurcation analysis and control of a discrete harvested prey-predator system with Beddington-DeAngelis functional response. (English) Zbl 1210.92062
The authors study a discrete prey-predator system with harvesting of both species and Beddington-DeAngelis functional response. By using the center manifold theorem and bifurcation theory, they establish that the system undergoes flip and Hopf bifurcations when the harvesting effort of the prey population passes some critical values. Numerical simulations exhibit period 6, 10, 12, 14, 20 orbits, cascades of period-doubling bifurcations in period 2, 4, 8, 16 orbits and chaotic sets. The numerically computed Lyapunov exponents confirm the complex dynamical behaviors. Moreover, a state delayed feedback control method, which can be implemented only by adjusting the harvesting effort for the prey population, is proposed to drive the discrete prey-predator system to a steady state.

MSC:
92D40 Ecology
39A28 Bifurcation theory for difference equations
93C95 Application models in control theory
37N25 Dynamical systems in biology
39A33 Chaotic behavior of solutions of difference equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
39A60 Applications of difference equations
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