Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
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.
scientific article; zbMATH DE number 5967331
scientific article