Dynamics analysis of a delayed diffusive predator–prey model with memory-based diffusion and fear effect of prey

In this paper, we propose a predator–prey model with memory-based diffusion, fear effect, generalist predator, maturation delay and memory delay. First, we obtain sufficient conditions for the existence of the positive equilibrium. Then, for the model without delays, we discuss the local stability of the positive equilibrium with or without diffusions. For the model with delays and without diffusions, we investigate the Hopf bifurcation induced by maturation delay. Next, for the model incorporating delays and diffusions, we apply the crossing curve methods to analyze the stability of the positive equilibrium and the existence of Hopf bifurcation. Finally, we show numerical simulations to verify the correctness of our findings.