A time-delayed predator-prey model with fear effect and stage structure

Abstract

The stability of a predator-prey model with two-stage structure and fear effect was studied. This model incorporated maturation time delay of the prey, and a delay differential equation model was established. By using the theory of the ordinary differential equations, the comparison theorem, the theory of the delay differential equations and the persistence theory of the infinite dimensional dynamical systems, the nonnegativity and boundedness of the solution of the model were proved, the conditions for the existence of the equilibria were given, the local asymptotic stability and the global asymptotic stability of the equilibria and the uniform persistence of the model were discussed. Numerical simulation was used to verify the correctness of the theoretical results, and it is concluded that the stability of the model changes when the fear effect and time delay are different.

Keywords

• predator-prey model
• fear effect
• stage structure
• uniform persistence