Study On Three Dynamics Of Species Food Chain With Hybrid Function Response

In ecosystem, all the species are interaction, so it is meaningful to research the dynamics of the species.In this article, three species food chain with hybrid functional response have been studied. Firstly, we briefly generalized the backgrounds and significances of the subject. Secondly, a three-species food chain with hybrid functional response composed with refuge and Leslie-Gower scheme has been researched. It has been proved that the system is bounded and the equilibria of the system are stable. By means of computer simulations, we discovered the complex dynamics of the system and demonstrated the chaotic behaviors. Moreover, the effects of the refuge scheme to the system were discussed. Then, a three-species food chain with hybrid functional response and improved Leslie-Gower scheme based on the above model has been researched. Existence and stability of the equilibria described by this system have been proved. By numerical simulation, we discovered the complex dynamics of the system. Finally, a ratio-dependent three-species food chain with Leslie-Gower scheme has been studied. We proved the existence and stability of the equilibria described by this system and researched the bifurcation of its subsystem. Furthermore, we discussed the effect of intra-specific competition scheme to the system,discovered the complex dynamics of the system by numerical simulation.