Related papers: Finite-size scaling in globally coupled phase osci…
The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting…
A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…
We study synchronization phenomenon in a self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value…
Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. Coupled…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…
Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation…
We study the finite-size scaling (FSS) property of the correlation ratio, the ratio of the correlation functions with different distances. It is shown that the correlation ratio is a good estimator to determine the critical point of the…
Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality…
We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction…
We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this…
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the…
We study the onset of synchronization in square lattices of limit cycle oscillators with long-range coupling by means of numerical simulations of the Kuramoto model. In this regime the critical coupling strength depends on the system size…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
We study an improved three-dimensional Ising model with external magnetic field near the critical point by Monte Carlo simulations. From our data we determine numerically the universal scaling functions of the magnetization, that is the…
In this paper, we study the applicability of an early warning index while studying the transitions to complete and generalized synchronizations in the coupled oscillator models using an unconventional system parameter and the coupling…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…