The Dynamics Properties Of The Nicholson Blowflies Model With Competition

In this thesis, we study a class of the Nicholson blowflies model with competi-tion, we obtain the following properties of solutions: existence、uniqueness、non-negativity、permanence, and the existence of the global solutions, the stabilities of the steady-state, the stability of the periodic solution, and a series of conclusions related to dynamics. The thesis is organized as follows;In the first chapter, we briefly recall the background of this model, works that have been made, the latest developments in this model. Meanwhile, we show our main contributions on this model. Moreover, we would list mathematical basic notions, definitions and preliminary used in the paper.In the second chapter, a steady-state equation which is equivalent to the equi-librium problem of the proposed model and several conclusions about the existence of positive equilibrium and boundary equilibrium will be achieved by using the technique of mathematical analysis.In the third chapter, by the results of chapter two and the classical stability theorem of functional differential equations, we show the stability and the attrac-tivity of the steady-state of our model; thus, on the views of mathematics, our model reveals the change law of the number of flying fly in two near area. In the third chapter, based on the results of the existence of steady-state, and together with the classical stability theorem of functional differential equations, several con-clusions concerned with the stability and the attractiveness of the steady-state of the proposed model have been made, and then reveal the regularity for number change of the two creatures in two near pathes.In the following two chapters, based on the study of previous sections, together with the functional analysis and the center manifold method, we have got more properties of Hopf bifurcation at the steady-state of the proposed model and its uniform persistent property of its dynamics.In the last chapter, using the matlab, we proceed with numerical simulation to verify the correctness of our theoretical results in this paper.