A Delayed Predator-Prey Model with Fear Effect and Cannibalism  

作　　者：Guoqing Li Xiaolin Lin Shaoyi Geng Guoqing Li;Xiaolin Lin;Shaoyi Geng(School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xian, China)

机构地区：[1]School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xian, China

出　　处：《Journal of Applied Mathematics and Physics》2025年第2期506-524,共19页应用数学与应用物理(英文)

摘　　要：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.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.

关 键 词：Predator-Prey Model Fear Effect CANNIBALISM Stability Hopf Bifurcation 

分 类 号：O17[理学—数学]