Nonequilibrium first-order phase transitions in the Kuramoto model in presence of inertia and noise

by Dr Shamik Gupta (Université Paris Sud)

Friday 12 Jul 2013, 14:30 → 15:30 Europe/Rome

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The Kuramoto model of coupled oscillators serves as a prototype to study spontaneous collective synchronization occurring in many biological and physical systems, e.g., yeast cell suspensions, pacemaker cell network in the heart, flashing fireflies, superconducting Josephson junction arrays, etc. The model involves overdamped motion of globally coupled oscillators of distributed natural frequencies. We study the model by including inertial terms and thermal noise in the dynamics. Inertial terms, for example, account for electrical capacitance of Josephson junction arrays, while thermal noise models the inevitable interaction with the environment. For unimodal frequency distributions, we study the dynamics in a reduced parameter space involving dimensionless mass, temperature, and width of the frequency distribution. We show that the dynamics exhibits a nonequilibrium first-order transition from a synchronized phase at low parameter values to an incoherent phase at high values. In proper limits, we recover the known continuous phase transitions in the Kuramoto model and in its noisy extension, and an equilibrium continuous transition in a related model of long-range interactions, the Hamiltonian mean-field model. Although effects of noise and inertia on the Kuramoto dynamics have been explored in the past, the complete phase diagram has not been investigated earlier. Our theoretical predictions are compared with extensive numerical simulations.