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Stability and Bifurcation Analysis in Shallow Lake Model with Delayed

Author: NanHaiShun
Tutor: WangHongBin
School: Harbin Institute of Technology
Course: Applied Mathematics
Keywords: Shallow lake eutrophication model Delay Differential Stability Hopf bifurcation
CLC: X524
Type: Master's thesis
Year: 2010
Downloads: 44
Quote: 0
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Abstract


Natural water eutrophication waters acceptance of excess nutrients ( such as nitrogen , phosphorus , etc.) lead to phytoplankton growth and reproduction . Shallow lake eutrophication model study of water quality dynamic changes of a more powerful tool to theoretical analysis , the results of experimental studies combine and apply to specific lakes , has gradually become a quite independent research methods . Most of the scholars of the past use of numerical simulation study of system dynamics is still rare . Shallow lake eutrophication model is a nonlinear system , the analysis of the kinetic properties of the stability of this model is to study the important issue of the shallow lake eutrophication models . In this paper , we first introduced the original shallow lake eutrophication models . Shallow lake eutrophication model with Delay in taking into account the phosphorus cycle there will be delays in the shallow lake system , our original shallow lake eutrophication model based on the time delay . So you can be more objective , more accurately reflect the actual work of the system , in order to achieve the ideal control phosphorus content in the lake . Therefore, an important theoretical and practical significance of shallow lake eutrophication model with time delay . Next , the research with Delay shallow lake eutrophication model kinetic properties , the balance point of the linear stability system stability analysis , when the characteristic roots of the characteristic equation of the linear part of the system corresponding pure imaginary roots , calculate the corresponding delay τ , the stability of the equilibrium point in time delay τ take some value flip and Hopf bifurcation at the equilibrium point system . Then use the normal form theory and the center manifold theorem discussed the stability of the Hopf bifurcation branch direction and bifurcation , given the stability of the solution on branch direction and branch cycle calculation formula . Finally , the corresponding numerical simulation using MATLAB software .

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CLC: > Environmental science, safety science > Environmental pollution and its prevention > Water pollution and its control > Lakes and reservoirs
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