The Dynamics Analysis Of An IGP Model

Intraguild predation(IGP) is a combination of competition and predation which is the most basic system in food webs that contains three species:resource(R),IG prey(C),IG predator(P).IG prey and IG predator predate on resource,At the same time,IG predator predate on IG prey. We formulate the intraguild predation model with Holling-Type I functional response between resource-IG prey and resource-IG predator,Holling-Type II functional response between IG prey and IG predator.We pro-vide sufficient conditions of the persistence of all possible scenarios for this model,which give us a complete picture on their global dynamic.In addition,the growth rate; of IG predator produces an effect on system dy-namic.When IG predator has a low growth rate,we treat IG predator as a constant value.We will have zero,one or two interior equilibriums.If the number of interior equi-librium is zero,one of boundary equilibriums is asymptotically stability.If the number of interior equilibrium is one,we can proof that it is likely to be satble. Also it is likely to be a saddle node bifurcation point or a Hopf bifurcation point.If the number of interior equilibrium is two,one of them can be stable at most.They also can be distable at the same time under certain conditions.When IG predator has a high growth rate,we have the same classification of interior equilibrium value.But it is more complicated in this condition.No matter how fast the rate IG predator grow.IGP model has coexistence of three species under certain conditions.The difference is the conditions that three species reach the coexistence state has.The same is that all the conditions are very strict.At last,the theoretical results obtained in this paper are not only tested but also extended by numerical simulations. We use a parameter ε represent the speed of IG predator grow. A set of reasonable parameter values for the full system are further chosen to numerically evaluate the potential impact of ε on the system dynamic.