title: Synchronization in populations of globally coupled oscillators with inertial effects
abstract: A model for synchronization of globally coupled phase oscillators including "inertial" effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized) and synchronized states of the oscillator population. Assuming a Lorentzian distribution of oscillator natural frequencies, g(Omega), both larger inertia or larger frequency spread stabilize the incoherent solution, thereby making it harder to synchronize the population. In the limiting case g(Omega)=delta(Omega), the critical coupling becomes independent of inertia. A richer phenomenology is found for bimodal distributions. For instance, inertial effects may destabilize incoherence, giving rise to bifurcating synchronized standing wave states. Inertia tends to harden the bifurcation from incoherence to synchronized states: at zero inertia, this bifurcation is supercritical (soft), but it tends to become subcritical (hard) as inertia increases. Nonlinear stability is investigated in the limit of high natural frequencies.
authors.affiliation: Escuela Politecnica Superior, Universidad Carlos III de Madrid, Avenida Universidad, 20 28911 Leganes, Spain and Dipartimento di Matematica, Universita di "Roma Tre," Largo San Leonardo Murialdo, 1 00146 Roma, Italy.
authors.initials: JA
authors.lastname: Acebron
authors.initials: LL
authors.lastname: Bonilla
authors.initials: R
authors.lastname: Spigler