Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
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DOI：
10.1016/j.nahs.2011.05.004
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发表时间：
2011-11-01
影响因子：
4.2
通讯作者：
Kar, T. K.
中科院分区：
文献类型：
--
作者：
Chakraborty, Kunal;Chakraborty, Milon;Kar, T. K.
In this paper, we analyze the dynamical behaviour of a bioeconomic model system using differential algebraic equations. The system describes a prey-predator fishery with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. It is observed that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest of harvesting is taken into account. We have incorporated a state feedback controller to stabilize the model system in the case of positive economic interest. A discrete-type gestational delay of predators is incorporated, and its effect on the dynamical behaviour of the model is analyzed. The occurrence of Hopf bifurcation of the proposed model with positive economic profit is shown in the neighbourhood of the coexisting equilibrium point through considering the delay as a bifurcation parameter. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations. (c) 2011 Elsevier Ltd. All rights reserved.
