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      • Theses - Department of Mathematics
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      Effect of time delays on the convergence speed of consensus dynamics

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      Embargo Lift Date: 2020-07-31
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      Author(s)
      Alhassan, Mohammed Kamil
      Advisor
      Atay, Mehmet Fatihcan
      Date
      2020-01
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      We discuss consensus problems under time delays. The presence of time delays results in an infinite-dimensional system rather than a system of ordinary differential equations. It has been shown that information transmission delays do not influence whether the system converges to a consensus value; however, further effects of delays are unknown. We show that time delays in most graphs decreases the convergence speed; while somewhat surprisingly, they can improve convergence in certain special graphs. We discuss the structure of graphs for which such improvement is possible.
      Keywords
      Consensus problems
      Time delays
      Convergence speed
      Undirected graphs
      Directed graphs
      Graph operations
      Normalized laplacian
      Stability
      Permalink
      http://hdl.handle.net/11693/52985
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      • Dept. of Mathematics - Master's degree 129
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