© 2019

Synchronization and Waves in Active Media

  • Nominated as an outstanding Ph.D thesis by the Technical University of Berlin, Berlin, Germany

  • Reviews mathematical reduction theory for continuous oscillator fields and discrete coupled oscillators

  • Describes the chemistry behind the oscillatory BZ reaction

  • Provides a tutorial on scientific computing on GPUs


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jan Frederik Totz
    Pages 1-12
  3. Jan Frederik Totz
    Pages 13-35
  4. Jan Frederik Totz
    Pages 37-54
  5. Jan Frederik Totz
    Pages 55-97
  6. Jan Frederik Totz
    Pages 99-101
  7. Back Matter
    Pages 103-164

About this book


The interplay between synchronization and spatio-temporal pattern formation is central for a broad variety of phenomena in nature, such as the coordinated contraction of heart tissue, associative memory and learning in neural networks, and pathological synchronization during Parkinson disease or epilepsy.
In this thesis, three open puzzles of fundametal research in Nonlinear Dynamics are tackled: How does spatial confinement affect the dynamics of three-dimensional vortex rings? What role do permutation symmetries play in the spreading of excitation waves on networks? Does the spiral wave chimera state really exist?

All investigations combine a theoretical approach and experimental verification, which exploit an oscillatory chemical reaction.  A novel experimental setup is developed that allows for studying networks with N > 1000 neuromorphic relaxation oscillators. It facilitates the free choice of network topology, coupling function as well as its strength, range and time delay, which can even be chosen as time-dependent. These experimental capabilities open the door to a broad range of future experimental inquiries into pattern formation and synchronization on large networks, which were previously out of reach.  


Chimera State Belousov-Zhabotinsky oscillators Spiral Waves Scroll Ring Excitable media Oscillatory Systems Synchronization and Entrainment Self-organized patterns Model of ventricular tachycardia,

Authors and affiliations

  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

Bibliographic information