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Delay Controlled Partial Synchronization in Complex Networks

  • Book
  • © 2019

Overview

Authors:
  1. Jakub Sawicki

    1. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

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  • Nominated as an outstanding Ph.D. thesis by the Technical University of Berlin
  • Includes a concise classification of multiplex networks and gives a brief introduction to bifurcation theory
  • Develops new analytical methods to predict synchronization with applications in neurosciences and music (organ pipes)
  • Provides measures to detect the novel phenomenon of partial synchronization patterns as double chimera states in triplex networks

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Jakub Sawicki
    Pages 1-7

  3. Complex Systems

    • Jakub Sawicki
    Pages 9-30

  4. Single-Layer Systems

    1. Front Matter

      Pages 31-31
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    2. Two Coupled Oscillators

      • Jakub Sawicki
      Pages 33-51

    3. Chimeras in Networks Without Delay

      • Jakub Sawicki
      Pages 53-70

    4. Interplay of Delay and Fractal Topology

      • Jakub Sawicki
      Pages 71-91

  5. Multilayer Systems

    1. Front Matter

      Pages 93-93
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    2. Partial Synchronization in 2-Community Networks

      • Jakub Sawicki
      Pages 95-114

    3. Multiplex Networks

      • Jakub Sawicki
      Pages 115-157

    4. Conclusion

      • Jakub Sawicki
      Pages 159-164

  6. Back Matter

    Pages 165-166
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Keywords

About this book

The focus of this thesis are synchronization phenomena in networks and their intrinsic control through time delay, which is ubiquitous in real-world systems ranging from physics and acoustics to neuroscience and engineering. We encounter synchronization everywhere and it can be either a helpful or a detrimental mechanism. In the first part, after a survey of complex nonlinear systems and networks, we show that a seemingly simple system of two organ pipes gives birth to complex bifurcation and synchronization scenarios. Going from a 2-oscillator system to a ring of oscillators, we encounter the intriguing phenomenon of chimera states which are partial synchrony patterns with coexisting domains of synchronized and desynchronized dynamics. For more than a decade scientist have tried to solve the puzzle of this spontaneous symmetry-breaking emerging in networks of identical elements. We provide an analysis of initial conditions and extend our model by the addition of time delay and fractalconnectivities. In the second part, we investigate partial synchronization patterns in a neuronal network and explain dynamical asymmetry arising from the hemispheric structure of the human brain. A particular focus is on the novel scenario of partial relay synchronization in multiplex networks. Such networks allow for synchronization of the coherent domains of chimera states via a remote layer, whereas the incoherent domains remain desynchronized. The theoretical framework is demonstrated with different generic models. 

Authors and Affiliations

  • Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Jakub Sawicki

About the author

Jakub Sawicki is a professional musician and physicist. His research is combining aspects of both fields. He studied music at Listaháskóli Islands University and University of Arts Berlin. Apart from his position as organist at Berlin Cathedral, Jakub Sawicki has deepened his studies of organ improvisation. He has engagements as choir and orchestra conductor and teaches improvisation at University of Arts Berlin. At the same time, he has continued his scientific research and received the Dr. rer. nat. degree from the Technical University Berlin. His research interests include synchronization phenomena in music, nonlinear delay differential equations, modeling of complex systems and neural dynamics.

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