We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator–prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.
['Israel Tankam', 'Plaire Tchinda Mouofo', 'Abdoulaye Mendy', 'Mountaga Lam', 'Jean Jules Tewa', 'Samuel Bowong']
Local Bifurcations and Optimal Theory in a Delayed Predator–Prey Model with Threshold Prey Harvesting