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Zbl 1245.92060
Chakraborty, Kunal; Chakraborty, Milon; Kar, T.K.
Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay. (English)
[J] Nonlinear Anal., Hybrid Syst. 5, No. 4, 613-625 (2011). ISSN 1751-570X

The dynamical behaviour of a bioeconomic model system of differential algebraic equations is analysed. The system describes a prey-predator fishery with two zones (free fishing and protected). It is shown that a singularity-induced bifurcation occurs when a variation of economic interest of harvesting is considered, thus the interior equilibrium changes from being stable to being unstable. A sufficient condition is obtained for the interior equilibrium to be stable when a state feedback controller is introduced. Further, when the time delay is incorporated as a parameter, Hopf bifurcation also occurs. Then these results are verified by some numerical simulations.
[Zhanyuan Hou (London)]

MSC 2000:: *92D40 Ecology
91B76 Environmental economics
34K18 Bifurcation theory of functional differential equations
34K60 Applications of functional-differential equations
65C20 Models (numerical methods)

Keywords: fishery; differential algebraic system; Hopf bifurcations

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