Bifurcation analysis and control of a discrete harvested prey-predator system with Beddington-DeAngelis functional response |
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| Authors: | Xue Zhang Qing-ling Zhang |
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| Institution: | a Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, Liaoning 110004, PR China
b Department of Electrical and Electronic Engineering University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia |
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| Abstract: | In this paper, we 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, we establish that the system undergoes flip bifurcation and Hopf bifurcation when the harvesting effort of prey population passes some critical values. Numerical simulations exhibit period-6, 10, 12, 14, 20 orbits, cascade of period-doubling bifurcation in period-2, 4, 8, 16 orbits and chaotic sets. At the same time, 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. |
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| Keywords: | Beddington-DeAngelis functional response Flip bifurcation Hopf bifurcation State delayed feedback control Chaos Lyapunov exponents |
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