TITLE:
A Delayed Predator-Prey Model with Fear Effect and Cannibalism
AUTHORS:
Guoqing Li, Xiaolin Lin, Shaoyi Geng
KEYWORDS:
Predator-Prey Model, Fear Effect, Cannibalism, Stability, Hopf Bifurcation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.2,
February
25,
2025
ABSTRACT: In this paper, we consider the fear effect and gestation delay, and then establish a delayed predator-prey model with cannibalism. Firstly, we prove the well-posedness of the model. Secondly, the existence and stability of all equilibriums of the system are studied. Thirdly, the Hopf bifurcation at the coexistence equilibrium is investigated, and the conditions for the occurrence of Hopf bifurcation at the unique positive equilibrium point of the system with delay are determined. Finally, the numerical simulation results show that as the time delay increases, the equilibrium loses its stability, and the system has periodic solution.