Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 347, Issue 7, Pages 1076-1096Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2010.03.016
Keywords
Beddington-DeAngelis functional response; Flip bifurcation; Hopf bifurcation; State delayed feedback control; Chaos; Lyapunov exponents
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Funding
- National Science Foundation of China [60974004]
- Natural Science Foundation of China [60904009]
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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. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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