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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…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
Models of Dynamical Electroweak Symmetry Breaking are expected to display a quasi-conformal scaling behaviour in order to accommodate experimental constraints. The scaling properties of a theory can be studied using finite volume…
Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network,…
We present an exploratory study of a gauge-invariant non-perturbative renormalization technique. The renormalization conditions are imposed on correlation functions of composite operators in coordinate space on the lattice. Numerical…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
We study the classical cubic-lattice double dimer model, consisting of two coupled replicas of the close-packed dimer model, using a combination of theoretical arguments and Monte Carlo simulations. Our results establish the presence of a…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
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 make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes…
We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…
The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the…
We study the thermal phase transitions of a generic real scalar field, without a $Z_2$-symmetry, referred to variously as an inert, sterile or singlet scalar, or $\phi^3+\phi^4$ theory. Such a scalar field arises in a wide range of models,…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…