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Dynamical Analysis in NICHOLSON Blowflies Equation with Two Delays

Author: ZhangXiangHua
Tutor: WeiJunJie
School: Harbin Institute of Technology
Course: Applied Mathematics
Keywords: Nicholson Drosophila model Equilibrium point Stability Periodic solution Hopf bifurcation
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 39
Quote: 0
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Abstract


Because of the the Drosophila growth cycle is very short , easy to carry out biological experiments . Therefore, whether in biology or in mathematics have appeared a lot of discussion about the Drosophila model . However, discussion of the most widely used Drosophila differential equation model is established by Nicholson . In this paper, with the nature of the dynamics of the two delays Nicholson Drosophila model fishing items Hx (t??) , Which delays ? Organism from larval development to grow up until the time fishing , H represents the intensity of the fishing coefficient. This paper Delay parameters, use of the stability of the positive equilibrium point of the model of local Hopf bifurcation theory , the existence of local Hopf bifurcation , and the nature of its branches were discussed in detail . This paper briefly describes the differential equations of the development process as well as the research background and research work . Then , Nicholson will be studied Drosophila model equations linearized , and discussion of the equation in the single - Delay and Delay both cases , the distribution of the root of the equation corresponding characteristic equation , the positive equilibrium point stability positive equilibrium point at the local Hopf bifurcation occurring conditions . Secondly, the use of the center manifold and regulatory theory discussed in the formula of the positive equilibrium point at the local Hopf bifurcation , and in order to discuss the direction of the local branch of the Hopf bifurcation , bifurcation stability of periodic solution cycle . Again, through the use of computers and MATLAB program numerical simulation of a strong support to the theoretical results previously obtained by calculation of the instance , and will happen stable positive equilibrium point model ? Parameters using MATLAB software resistance switching phenomenon . The last part of the conclusion it throughout the main results of the paper are summarized .

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