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Stability and Bifurcation Analysis on Delay Differential Equations

  • Author / Creator
    Lin, Xihui
  • Most recent studies on delay differential equations are mainly focused on local stability analysis, stability switches, and local existence of Hopf bifurcations with only one delay included, while the global existence of Hopf bifurcation and stability analysis with two delays are hardly discussed. In this thesis, we numerically explore global behaviors of Hopf branches arising from where the characteristic roots crossing the imaginary axis, and we reveal that there seems to be a strong and simple underlying rule, which is been partly studied by Li and Shu in their recent paper [Li & Shu 2010a]. In addition, stability analysis on delay differential equations with two discrete delays will also be studied. We extend the work by [Guet al.2005], and establish a similar theory on a more general type of models. Finally, we provide some preliminary results for the two-delay models with parameters depending on one delay.

  • Subjects / Keywords
  • Graduation date
    2012-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3ND31
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Wang, Hao(Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Han, Bin(Department of Mathematical and Statistical Sciences)
    • Wang, Hao(Department of Mathematical and Statistical Sciences)
    • Ru, Chong-Qing(Department of Mechanical Engeering)