A Delayed Fractional-Order Predator–Prey Model with Three-Stage Structure and Cannibalism for Prey

In this study, we investigate a delayed fractional-order predator–prey model with a stage structure and cannibalism. The model is characterized by a three-stage structure of the prey population and incorporates cannibalistic interactions. Our main objective is to analyze the existence, uniqueness, boundedness, and local stability of the equilibrium points of the proposed system. In addition, we investigate the Hopf bifurcation of the system, taking the digestion delay of the predator as the branch parameter, and clarify the necessary conditions for the existence of the Hopf bifurcation. To confirm our theoretical analysis, we provide a numerical example to validate the accuracy of our research results. In the conclusion section, we carefully review the results of the numerical simulation and propose directions for future research.