Hamiltonian mean field model: Effect of network structure on synchronization dynamics
Yogesh S Virkar1, Juan G Restrepo2, James D Meiss2
1Department of Computer Science, University of Colorado at Boulder, Boulder, Colorado 80309, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
Summary
Synchronization in coupled rotor systems depends on network structure. Synchrony emerges when coupling strength relates to network connectivity, with heterogeneity impacting early stages but large coupling ensuring robustness.
Area of Science:
- Physics
- Complex Systems
- Network Science
Background:
- The Hamiltonian mean field (HMF) model describes conservative dynamics in systems with long-range interactions.
- Coupled inertial rotors serve as a prototype for studying synchronization phenomena.
Purpose of the Study:
- To investigate the influence of network structure on the synchronization of coupled inertial rotors.
- To analyze the role of network heterogeneity in the transition to synchrony.
Main Methods:
- Linear stability analysis of the incoherent state.
- Derivation of a closed system of equations for local order parameters.
- Numerical simulations on Erdös-Renyi and power-law networks.
Main Results:
- The transition to synchrony is initiated when the coupling constant (K) is inversely proportional to the largest eigenvalue of the adjacency matrix.
- Network heterogeneity significantly affects the degree of synchronization just beyond the transition point.
- For large coupling constants (K), synchronization becomes robust to variations in network degree distribution.
Conclusions:
- Network topology critically influences the onset and degree of synchronization in Hamiltonian mean field systems.
- Understanding network heterogeneity is key to predicting synchronization behavior in complex systems.
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