Stability analysis of a predator-prey model with stage structure

Abstract

Many scholars have explored the population dynamics system, functional response, time-delay response, and so on. Based on the existing research, this paper studies a class of predator-prey models with stage structure, time delay, and Holling type-II functional response function. The stability of that model at the positive equilibrium point, the sufficient condition for stability, and the existence of Hopf bifurcation are discus. The model was numerically simulated by taking appropriate parameters and different time delay values, variation diagram of each component, and solution curves were given near the critical value. The results show that the stability of the system will change with the variation of the bifurcation parameter value, and Hopf bifurcation will occur.