Global Coupling Visualization
In globally coupled map lattices, each site interacts with the global average of all sites. This creates fascinating synchronization phenomena and collective behavior.
Interactive global CML visualization will be available here
Synchronization Phenomena
Global coupling leads to various synchronization states and collective dynamics that emerge from the interaction between local chaos and global order.
- • Complete synchronization
- • Phase synchronization
- • Cluster synchronization
- • Chimera states
- • Synchronization transitions
Global Coupling Strength
The global coupling parameter ε controls how strongly each site is influenced by the collective state of the entire system.
- • Weak coupling: Independent chaotic dynamics
- • Moderate coupling: Intermittent synchronization
- • Strong coupling: Full synchronization
- • Critical coupling values
Mathematical Framework
Global Coupled Map Lattice:
x_i(t+1) = (1-ε)f(x_i(t)) + ε/N Σ f(x_j(t))
Ott-Antonsen Ansatz
Powerful theoretical framework for understanding synchronization in large systems of globally coupled oscillators.
Kuramoto Model
Classic model for synchronization in globally coupled phase oscillators, related to coupled map lattices.
Network Theory
Global coupling represents the special case of a complete graph in complex network theory.