Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
arXiv:1706.06316 · doi:10.1088/1751-8121/aa88d7
Abstract
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.
arXiv commentInvited contribution to the J. Phys. A Special Issue "Emerging Talents" http://iopscience.iop.org/journal/1751-8121/page/Emerging-Talents; v2: minor revision, close to the published version
References in corpus (41)
- Chimera States for Coupled Oscillators
- The Kuramoto model in complex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Chimera States in Mechanical Oscillator Networks
- Solvable model for chimera states of coupled oscillators
- Long Time Evolution of Phase Oscillator Systems
- Macroscopic description for networks of spiking neurons
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Physics of the rhythmic applause
- Chimera states: The Existence Criteria Revisited
- Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
- Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
- Breaking of ergodicity and long relaxation times in systems with long-range interactions
- Thermodynamics and dynamics of systems with long-range interactions
- Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
- Low-dimensional dynamics of populations of pulse-coupled oscillators
- Intermittent chaotic chimeras for coupled rotators
- Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
- From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
- Chimera states in two populations with heterogeneous phase-lag
- Heterogeneity of time delays determines synchronization of coupled oscillators
- Time delay in the Kuramoto model with bimodal frequency distribution
- Dynamics and thermodynamics of rotators interacting with both long and short range couplings
- The world of long-range interactions: A bird's eye view
- Nonequilibrium first-order transition in coupled oscillator systems with inertia and noise
- Bifurcations and singularities for coupled oscillators with inertia and frustration
- On the equivalence of phase-oscillator and integrate-and-fire models
- Synchronization transitions in globally coupled rotors in presence of noise and inertia: Exact results
- The Brownian Mean Field model
- One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes
- A minimal model of partial synchrony
- Dynamics of a population of oscillatory and excitable elements
- Models with short and long-range interactions: phase diagram and reentrant phase
- Nonstandard transitions in the Kuramoto model: A role of asymmetry in natural frequency distributions
- Overdamped dynamics of long-range systems on a one-dimensional lattice: Dominance of the mean-field mode and phase transition
- Synchronization in Complex Systems Following the Decision Based Queuing Process: The Rhythmic Applause as a Test Case
- Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems
- Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity
- Dynamics of coupled oscillator systems in presence of a local potential
Cited by in corpus (4)
- Spontaneous synchronization and nonequilibrium statistical mechanics of coupled phase oscillators
- Synchronization Behavior in a Ternary Phase Model
- Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions
- Exact correlations in the nonequilibrium stationary state of the noisy Kuramoto model