Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2107.09711

Synchronization transition in the two-dimensional Kuramoto model with dichotomous noise

Mrinal Sarkar
View original source ↗Read source document ↗Export metadata ↓

Abstract

We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest neighbor interactions and dichotomous noise. In the nonequilibrium stationary state attained at long time, the model exhibits a Berezinskii-Kosterlitz-Thouless ($BKT$)-like transition between a phase at low noise amplitude characterized by quasi long-range order (critically ordered phase) and algebraic decay of correlations and a phase at high noise amplitude that is characterized by complete disorder and exponential decay of correlations. The interplay between the noise amplitude and the noise correlation time is investigated, and the complete, nonequilibrium stationary-state phase diagram of the model is obtained. We further study the dynamics of a single topological defect for various amplitude and correlation time of the noise. Our analysis reveals that a finite correlation time promotes vortex excitations, thereby lowering the critical noise amplitude of the transition with an increase in correlation time. In the suitable limit, the resulting phase diagram allows to estimate the critical temperature of the equilibrium $BKT$ transition, which is consistent with that obtained from the study of the dynamics in the Gaussian white noise limit.

Explore related subjects

nlin.AO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mrinal Sarkar. 2021-08-02. Synchronization transition in the two-dimensional Kuramoto model with dichotomous noise. https://doi.org/10.1063/5.0056001

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Deviations from global coupling in adaptive oscillator networks: a mean-field theory for the variance of coupling weights

A wide range of physical and biological systems are adaptive networks, in which the dynamics of the nodes and of the edges connecting them co-evolve. Mean-field reductions of such systems typically track only the average coupling strength, and therefore cannot determine when the coupling stays effectively homogeneous and when structured connectivity emerges. Here, we present a second-order moment closure that allows us to derive mean-field equations for the coupling-weight variance in networks of heterogeneous phase oscillators with adaptive coupling, starting from uniform coupling weights. In agreement with network simulations, we find a nonlinear, non-monotonic dependence of the relative weight variance on the oscillator heterogeneity that is mediated by the phase coherence. Moreover, we find that deviations from global coupling strongly depend on an interaction between the oscillator heterogeneity and the adaptation rule. Whereas symmetric adaptation causes a strongly coupled core of coherent oscillators to emerge and creates a bistable regime that is absent without adaptation, antisymmetric adaptation leads to antisymmetric coupling within the same core, thereby destabilizing it. Our equations therefore delineate the regimes in which adaptive networks behave like globally coupled systems from those in which more complex coupling patterns form.

nlin.AO↗
arXiv2026

Self-Organization to the Edge of Ergodicity Breaking in a Complex Adaptive System

Self-organized criticality is widely invoked for collective behavior, yet its role in objective-driven, heterogeneous adaptive systems is unclear. We introduce {\tt EvoSK}: agents learn on a Sherrington--Kirkpatrick landscape while the least fit are replaced. It self-organizes to the edge of ergodicity breaking, with scale-free avalanches ($τ\approx -1.5$) and rewards beating any tuned non-evolutionary regime. Its cascade's branching ratio is the spectral radius of the learning dynamics' Jacobian, making critical branching and ergodicity breaking one marginal-stability condition fixing the exponent. The attraction to criticality follows from the selection--mutation balance: subcritical cascades decay too fast to dislodge frozen agents, supercritical cascades shield them from selection; only the critical power-law tail supplies the polynomial rate the balance requires.

nlin.AO↗
arXiv2026

When higher-order interactions enhance synchronization: the case of the Kuramoto model

Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled oscillators, traditionally assuming pairwise interactions. However, many real-world systems exhibit group and many-body interactions, which can be effectively modeled through hypergraphs. Here we show that the effect of such higher-order interactions on synchronization is non-monotonic. Through a numerical study of higher-order Kuramoto models on random hypergraphs and on globally coupled systems, we find that the degree of synchronization reached from incoherent initial conditions is maximized at a small but nonzero higher-order coupling strength: weak higher-order interactions enhance synchronization when added to pairwise ones, whereas strong ones work against it, in line with earlier reports of reduced basins and of cluster states. We further show, through a cost-constrained allocation analysis, that under a constrained budget for interactions a mixed allocation of pairwise and higher-order couplings consistently achieves higher synchronization than relying on either type alone. These findings clarify the role of higher-order interactions in shaping collective dynamics and point to design principles for optimizing synchronization in complex systems.

nlin.AO↗