Related papers: Critical exponents in coupled phase-oscillator mod…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
The importance of pulse-coupled oscillators (PCOs) in biology and engineering has motivated research to understand basic properties of PCO networks. Despite the large body of work addressing PCOs, a global synchronization result for…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
We study fidelity susceptibility in one-dimensional asymmetric Hubbard model, and show that the fidelity susceptibility can be used to identify the universality class of the quantum phase transitions in this model. The critical exponents…
We investigate emergence of the global collective behavior in networks of diffusively coupled identical oscillators, which in the established model is an invariant manifold of the motion equations. The interaction is modeled with the graph…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We consider a population of two-dimensional oscillators with random couplings, and explore the collective states. The coupling strength between oscillators is randomly quenched with two values one of which is positive while the other is…
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…
We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is…
We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is…
The linear response is studied in globally coupled oscillator systems including the Kuramoto model. We develop a linear response theory which can be applied to systems whose coupling functions are generic. Based on the theory, we examine…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…
The phenomenological universalities (PU) are extended to include time-depended quantum oscillatory phenomena, coherence and supersymmetry. It will be proved that this approach generates minimum uncertainty coherent states of time-dependent…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that…
Various phase transitions in models for coupled charge-density waves are investigated by means of the $\epsilon$-expansion, mean-field theory, and Monte Carlo simulations. At zero temperature the effective action for the system with…