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Synchronization of Coupled Oscillators

[latexpage]

To-Do:

  • Make adjacency matrices for different networks

Reference

  • Mason and Verwoerd (2006)

Applications

  • Spike-timing dependent plasticity and learning/memory
  • Permanent changes in synchronization after novel experiences
    • e.g., fear-based learning (hippocampus and amygdala)
  • Spatiotemporal patterns
    • “Language” of neurons
    • Mechanism of information flow throughout the brain
    • Dynamics of interactions between different regions
      • Dynamic coupling between brain regions (e.g., active or attentive behavior) gives rise to perception, movement, consciousness, etc.

Main Issue: Scale at which synchronization occurs

My own thoughts:

  • Scales with respect to size: “universal” → “galactic” → solar systems → planets, stars, asteroids, etc. → anatomical → cellular → subcellular → atomic → subatomic (quantum)

Kuramoto Model

\dot { \theta _{ i } } =\omega_i+\frac{K}{N}\sum _{j=1}^{N}{ \sin(\theta_j-\theta_i) }

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