an:05822363
Zbl 1210.92062
Zhang, Xue; Zhang, Qing-Ling; Sreeram, Victor
Bifurcation analysis and control of a discrete harvested prey-predator system with Beddington-DeAngelis functional response
EN
J. Franklin Inst. 347, No. 7, 1076-1096 (2010).
00266277
2010
j
92D40 39A28 93C95 37N25 39A33 65L12 65C20 39A60
flip bifurcations; Hopf bifurcations; state delayed feedback control; chaos; Lyapunov exponents
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.
Bilender P. Allahverdiev (Isparta)