Bifurcation dynamics in a modified Leslie type predator-prey model with predator harvesting and delay

In this article, the bifurcation behaviors of a modified Leslie type predator- prey model with harvesting and gestation delay of predator are discussed. The model takes the form of delayed differential-algebra equations. First, the existence of Hopf bifurcations in the model is studied by choosing the delay as a bifurcation parameter. It reveals that a sequence of stability switches and Hopf bifurcations can occur as the delay increases monotonously from zero. Next, the direction of the Hopf bifurcations and the stability of the bifurcating periodic orbits are also investigated. Moreover, we present several numerical simulations to support the theoretical results with the help of Matlab software. Lastly, the significances of our findings are discussed.