Delay Controlled Partial Synchronization in Complex Networks

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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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. 

• Synchronization in complex systems
• Physics of Organ Pipes
• Control By Delay
• Complex Networks in neuroscience
• Chimera States
• Partial Synchronization
• Multiplex Network

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

  Jakub Sawicki

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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