Non-selective harvesting in prey--predator models with delay
The authors study the following two delayed prey-predator models with nonselective harvesting: \[ \begin{aligned} \frac{dx}{dt} & = xg(x(t-\tau))-yp(x)-q_1E_1x, \\ \frac{dy}{dt} & = y[-d+\alpha p(x)]-q_2E_2y, \end{aligned} \] and \[ \begin{aligned} \frac{dx}{dt} & = xg(x)-yp(x)-q_1E_1x, \\ \frac{dy}{dt} & = y[-d+\alpha p(x(t-\tau))]-q_2E_2y. \end{aligned} \] Sufficient conditions for the stability of the only interior equilibrium are established. When this equilibrium loses stability, Hopf bifurcation will occur. These results indicate that the time delay may cause a stable equilibrium to become unstable and even a switching of stability, on the other hand, harvesting effort has a stabilizing effect on the equilibrium if it is under the critical harvesting effort level.
scientific article; zbMATH DE number 5069041
scientific article