Predator-prey Dynamics With A Fear Effect

Predator-prey interactions are a natural phenomenon in ecosystems,and mastering the dynamic behavior between them plays an important role in maintaining the balance of ecosystems.Based on the predator-prey system with group defense,the effect of fear effects on the population kinetic behavior of the predator-prey model was considered in Chapter 2.In chapter 3,it is further considered that intraspecific competition among predators due to lack of food,water,competition for mates,etc,the predator-prey model with fear effect and group defense and intraspecific competition of predator has been established.For the established prey with fear effect and group defense of predator-prey model,analyzed the existence of the non-negative equilibrium point,using the linearization method analyzed the boundary equilibrium behavior,the zero near the rail properties and the stability of the internal balance point,conditions for phyloenic Hopf bifurcation,the results show that enhanced fear effect will make predator population decreased,more in line with biological reality,predator and prey can be stable survival.For the established prey with fear effect and group defense and predator intraspecific competition predator-prey model,analyzes the existence of the system and the stability of the equilibrium point under certain conditions,we prove that the system does not have a limit cycle under certain conditions,and analyze the Hopf bifurcation of the system.