Predator-prey System Fear Effect

In this thesis,considering the Beddington-DeAngelis?B-D?functional response into the Predator-Prey system with prey fear effect,a new model is established and its dynamical properties are analyzed.The existence conditions of equilibrium are given.And by using the Hurwitz criterion,constructing Lyapunov function or Dulc function,the local and global stability of the equilibria are analyzed.In addition,the fear effect has a double-sided effect on the prey,which reduces the prey's birth rate and also enhances the predation ability of the prey.A new model is constructed to describe this phenomenon,and an adaptive dynamics method is used to estimate the fear level of the prey.The stable state of evolution was analyzed.In the first chapter,we introduces the development of prey-predator systems and biological fear factors,and introduces the relevant theoretical knowledge used in the paper.In chapter 2,we considers a predator-prey model with B-D functional response and fear effect.By using the Hurwitz criterion,constructing Lyapunov function and Dulac function to analyze the model,we can see that the newly introduced parameter q₂will affect the equilibrium state of the system.The increase of q₂is beneficial to the stability of the system,and when q₂decreases,the system may lose its stability.The other numerical simulation results also explain the parameters and possible phenomena that have no analytical solution.In the third chapter,we introduces the effect of fear effect on predation rate.When the fear effect is zero,the contact rate between prey and prey is the predation rate.The existence of fear effect will correct the predation rate,and the increase of fear effect will reduce the predation rate.By applying the theory of stability theorem,a global positive equilibrium point is obtained.By using the adaptive dynamics method,the continuous stability and evolutionary branch conditions of the singularity strategy for the evolution of fear intensity in prey are given.In the last chapter,we briefly reviews the conclusions in the article,highlights the biological significance of the research content of this article,analyzes some of the deficiencies in the article and places for improvement,and proposes some issues and work that need further study.