Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4976055 | Journal of the Franklin Institute | 2010 | 21 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Signal Processing
Authors
Xue Zhang, Qing-ling Zhang, Victor Sreeram,