Dynamics Of Food Chain Models With Stage Structure

In this paper, two predator-prey chain modes modeling evolution of three pop-ulations with stage structure in ecology are established. Using the theory of delay differential equation and dynamical system, the stability of two models are studied. The whole paper consists of three chapters.The first chapter is the introduction. The background and significance of popula-tion dynamics are briefly addressed, Introduces some multi-population phenomena of predation in the ecological system and the reproduction and predation rules between the ecological species, to lay a good foundation for the later study, and the main results of the thesis is introduced, stability analysis of food chain models with stage structure. Finally, some lemmas to be used in this thesis are given.In the second chapter, A three species predator-prey food chain model with stage structure is discussed, in which the third species is the predator of the second one and the second species is the predator of the first one. The second species is divided into two classes:the immatures and matures. Assume that the immature species hiding in the cave, it not only can not prey but also can not be capture. By analyzing characteristic equations of the linearization system of the equilibria, constructing the Lyapunov functional and using an iterative technique, a set of sufficient conditions are derived to ensure the local and global stability of the equilibria of the model. Finally, numerical simulations are given to verify the theoretical analysis.In the third chapter, we assume that at the top of the food chain food source is not a single species population, and put the death of rate and intra-species competition rate of the mature second species separate consideration, this expands the model of the second chapter. By analyzing characteristic equations of the linearization system of the equilibria, constructing the Lyapunov functional and using an iterative technique, a set of sufficient conditions are derived for the local and global stability of the nonnegative equilibria to ensure the model. Finally, numerical simulations are given to verify the theoretical analysis.