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Three ecological model Hopf bifurcation , stability and durability

Author: DengZhiJian
Tutor: ChenSiYang
School: Shaanxi Normal University
Course: Applied Mathematics
Keywords: Hopf bifurcation Unconditional stability Predator-prey Feedback control Persistent
CLC: O175.7
Type: Master's thesis
Year: 2011
Downloads: 19
Quote: 0
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Abstract


Periodic differential equations , stability and durability, reveals the long-term behavior of dynamical systems , has a wide application in ecology where , for maintaining ecological balance, to save endangered biological species has a very important practical significance . Along, differential equations to describe the biological laws phenomenon , has a strong practical background in the formation of new issues also will be discussed in this paper three ecological model Hopf bifurcation , stability and durability, including: a class of Generalized Logistic Model the Hopf bifurcation , cannibalism rate on the predator-prey model stability and N A group feedback control system persistence second chapter , we study a class of generalized ecological model with delays positive equilibrium stability and Hopf existence and uniqueness . Firstly, according to the unconditional stability of linear systems and eigenvalue theory, sufficient conditions for local stability of the model unconditionally ; then, using the theory of orthogonal function model is discussed existence and uniqueness of Hopf bifurcation ; Finally, an example verifies theorem and conclusions can be realized by using Matlab solution curve fitting diagram given third chapter mainly discusses cannibalism rate of population structure model for a class of dynamic effects , and draws cannibalism rate Hopf bifurcation threshold. Firstly eigenvalue theory and Lyapunov direct method for linear stability analysis, and affect the stability of the parameters are discussed , followed by verification of cannibalism stabilizing effect on the population , and was predator growth was the opposite. Finally Matlab numerical simulations further validate the theory can be realized . fourth chapter discusses a class of delay and periodic functions with ω N- species persistence feedback control system according to ω periodic function of the nature of the comparison of the use of differential equations theory , feedback control system is given persistent condition .

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