Dynamics Analysis Of An IGP Model With Holling-? Functional Response

Intraguild predation(IGP),the interaction between species that predate and com-pete for shared resources,is a common species phenomenon in many ecological systems.It is very important for biological prevention and control.In order to realize its guiding role in practical application,an IGP model which incorporates the Holling-II functional response functions is established in this paper.We investigated the dynamical behav-iors of these models and the primarily contents of this dissertation are listed as follows:Firstly,the existence and stability of equilibria are studied.The global asymptotic stability of equilibria are discussed in the two dimensional subsystem by applying the Lyapunov stability method.The sufficient conditions are obtained for the stability of boundary equilibria.According to the definition of persistence,we received the sufficient conditions of persistence.Then,the numerical simulations are applied to the model under the given values of parameters to obtain the dynamics of system totally.The numerical results show that the system may have an attracting invariant torus but no positive equilibrium in R+3 Furthermore,the Poincare map and Fourier transform spectrum analysis are performed to study the complex dynamics of the system on the invariant torus.The results suggest that the dynamics on the invariant torus is almost periodic.Finally,we obtain a normal form to analyze the formation mechanism of invariant torus if e1(?+1)[?1+1(?1+1)2]?4e2[2?1+?2(?1-1)].During the study of the normal form,the results imply that there is a stable limit cycle in the normal form.Therefore it means that there will be an attracting invariant torus in the original system.