title: Hamiltonian mean field model: Effect of network structure on synchronization dynamics.
abstract: The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions.
authors.affiliation: Department of Computer Science, University of Colorado at Boulder, Boulder, Colorado 80309, USA.
authors.forename: Yogesh S
authors.initials: YS
authors.lastname: Virkar
authors.affiliation: Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0526, USA.
authors.forename: Juan G
authors.initials: JG
authors.lastname: Restrepo
authors.affiliation: Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0526, USA.
authors.forename: James D
authors.initials: JD
authors.lastname: Meiss