Based on the niche theory,a class of delayed intraguild predation systems integrating Holling type I and type II functional response functions is constructed.Firstly,the existence conditions of the positive equilibriu...Based on the niche theory,a class of delayed intraguild predation systems integrating Holling type I and type II functional response functions is constructed.Firstly,the existence conditions of the positive equilibrium point of the system are clarified.Secondly,the dynamic behavior of the system is analyzed from two aspects:in the absence of time delay,the local stability of the positive equilibrium point of the system is analyzed by using the Hurwitz criterion.In the presence of time delay,with the gestation delay of the predator population as the bifurcation parameter,the existence of Hopf bifurcation near the positive equilibrium point of the system is explored,and the properties of Hopf bifurcation are analyzed by means of the center manifold theorem and normal form theory.Finally,the correctness of the theoretical derivation is verified by numerical simulation.展开更多
文摘Based on the niche theory,a class of delayed intraguild predation systems integrating Holling type I and type II functional response functions is constructed.Firstly,the existence conditions of the positive equilibrium point of the system are clarified.Secondly,the dynamic behavior of the system is analyzed from two aspects:in the absence of time delay,the local stability of the positive equilibrium point of the system is analyzed by using the Hurwitz criterion.In the presence of time delay,with the gestation delay of the predator population as the bifurcation parameter,the existence of Hopf bifurcation near the positive equilibrium point of the system is explored,and the properties of Hopf bifurcation are analyzed by means of the center manifold theorem and normal form theory.Finally,the correctness of the theoretical derivation is verified by numerical simulation.
