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Two species discrete autonomous model of competition and predation

Author: ChenGuangYe
Tutor: ZuoZhiDong
School: Xinjiang University
Course: Computational Mathematics
Keywords: Discrete Competition Predator - prey Global Stability Bifurcation theory
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 49
Quote: 0
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Abstract


Discrete dynamical behavior of two species of autonomy is an important biological areas of mathematical research , in some cases, than the continuous-time population model which model is more realistic. This paper studies the discrete autonomous competition model and the proportion of two species dependent predator - prey model . Using the iterative method and comparison principle be balanced under appropriate conditions, the global stability , and the use of the center manifold and bifurcation theory we get more complex dynamical behavior . The main contents are as follows : Chapter 1 is an introduction , describes the dynamic behavior of two species of discrete autonomous research background , purpose and significance , given the discrete dynamic behavior of two species status and results. Finally, this organizational structure. Section 2 of prior knowledge to use this article gives some lemmas Section 3 discusses the discrete autonomy in competitive dynamics of the discrete model : local stability of the equilibrium point , global stability , model Flip branch , Hopf bifurcation and chaos . Finally, some numerical examples, the numerical simulation to verify the correctness of the theorem . Section 4 discusses two groups ratio dependent predator - prey dynamics of the discrete model : local stability of the equilibrium point , global stability , model Flip branch , Hopf bifurcation and chaos . Finally, some numerical examples, the numerical simulation to verify the correctness of the theorem . Section 5 we give a summary and discussion .

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