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Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay. (English) Zbl 1245.92060
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.

MSC:
92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
34K18 Bifurcation theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
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