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The Application of Differential Equation in Some Kinds of Ecosystem

Author: LiJuChen
Tutor: ZhuoXiangLai
School: Shandong University of Science and Technology
Course: Applied Mathematics
Keywords: predator-prey system limit cycles closed orbit equilibrium point stability deviating argument periodic solution
CLC: O175
Type: Master's thesis
Year: 2009
Downloads: 63
Quote: 0
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Abstract


There are four chapters in this thesis.The first chapter is overview, in which we introduce the developing status about Mathematical Ecology and some related works that we have done.In the second chapter, we study a class of 2n +1 degree Kolmogorov’s system. The system is discussed mainly about some sufficient conditions to ensure the system has no limit cycle and the stability of equilibrium, the sufficient conditions of existence of a stable limit cycle of the system in the first quadrant.In the third chapter, we discuss a class of predator-prey system with Holling II type functional response .The natures of equilibrium points are discussed. The sufficient conditions of nonexistence of the closed orbit and conditions of existence of the unique and stable limit cycle are also obtained. Then, we study the effect of prey influx on the predator-prey system with Holling II type functional response. The impact on the stability and equilibrium density is mainly discussed.In chapter 4, with the help of the continuation theorem of the coincidence degree and differential inequalities, we study two kinds of third order functional differential equation with deviating argument. Sufficient conditions for the existence of periodic solutions are obtained. Our work generalizes the corresponding work of the past.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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