Bifurcation Analysis of a Delayed Predator–Prey Model With Square Root Response Functions

In this paper, a delayed predator–prey model with a square root functional response is structured and analyzed. Through a discussion of the time delay and an analysis of the characteristic equations, the local stability of the boundary equilibrium and the positive equilibrium and the existence of Hopf bifurcation are investigated. On this basis, the critical value of the Hopf bifurcation is derived. According to the central manifold theorem and normal form theory, the nature of the Hopf bifurcation is obtained. Finally, by conducting numerical simulations, it is observed that incorporating a time delay can influence the stability of the predator and prey populations, causing periodic oscillations in the number of two populations.