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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.
91B76Environmental economics (natural resource models, harvesting, pollution, etc.)
34K18Bifurcation theory of functional differential equations
34K60Qualitative investigation and simulation of models
65C20Models (numerical methods)
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