Dynamics on Networks 2

1. Synchronization:
   • Examples: firefly, fireflies, heart pacemaker cells, cicada
   • The Kuramoto model (Java Applet by Albert Diaz-Guilera) (Cactus Applet)
   • Collective synchronization
2. Biological Patterns:
   • Morphogenesis is the process whereby a living organism develops form and structure, e.g.
   • Where do spots come from? Turing's answer
     • Turing, A. M. "The Chemical Basis of Morphogenesis." Bulletin of Mathematical Biology 52, no. 1–2 (1990): 153–97
     • Applet: 1-dimensional instability
     • Reaction-Diffusion equations
     • Constraints for a finite wave-length instability
     • Long-range inhibition & short-range excitation

Some Related Links

Synchronization

• Firefly (flash synchrony)
• Steven Strogatz on sync

Morphogenesis

• Visual Models of Morphogenesis
• Reaction Diffusion Equations and Animal Coat Patterns
• Morphological processes and reaction-diffusion systems
• Theoretical aspects of pattern formation and neuronal development (MPI Tübingen)
• Primary pattern formation, organizing regions and regeneration (MPI Tübingen)
• Modelling Pigmentation Patterns
• The Alan Turing Internet Scrapbook Growth, Form and Crisis

(Detailed Lecture Notes (PDF))