Relationships between network connectivity and global dynamics of complex dynamical systems

  • Author / Creator
  • The global dynamics of complex systems is investigated in this thesis, using the framework of coupled dynamical systems. For a coupled dynamical system on an interaction network, we show the impact of the connectivity of the interaction network on its dynamical behavior. We lay particular emphasis on non-strongly connected interaction networks, and clustered behavior of coupled dynamical systems. Two typical kinds of coupled dynamical systems are studied in the thesis: coupled gradient systems and coupled oscillators. We present a general approach to investigating the dynamical behaviors of coupled gradient systems. The approach is demonstrated through two multi-group epidemic models: one ordinary differential equation model and one functional differential equation model with distributed delay. We show disease either persists in all groups of one strongly connected component or dies out in all groups of one strongly connected component. Moreover, we present a threshold value that determines whether disease persists or dies out in one strongly connected component. We study both coupled linear and nonlinear oscillators in the thesis. For systems of coupled linear oscillators, we show its dynamical behavior under arbitrary interaction networks. When the interaction network is strongly connected, synchronization occurs; otherwise, clustered behavior may occur. In the case of clustered behavior, we show the frequency of oscillators in the same strongly connected components are the same. For systems of coupled nonlinear oscillators, synchronization occurs when its interaction network is strongly connected; otherwise, we show synchronization can occur when the coupling strength between any two strongly connected components is sufficiently large. For coupled gradient systems and coupled oscillators, our analysis shows synchronization occurs under strongly connected interaction networks; while non-strongly connected interaction networks give rise to clustered behavior. In the case of clustered behavior, local systems in one strongly connected components are in the same dynamical cluster.

  • Subjects / Keywords
  • Graduation date
    Spring 2016
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • 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
  • Institution
    University of Alberta
  • Degree level
  • Department
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
  • Examining committee members and their departments
    • Xingfu Zou (Department of Applied Mathematics, University of Western Ontario)
    • Hao Wang (Department of Mathematical and Statistical Sciences)
    • James Muldowney (Department of Mathematical and Statistical Sciences)
    • Bin Han (Department of Mathematical and Statistical Sciences)
    • Anthony T-M Lau (Department of Mathematical and Statistical Sciences)