Related papers: Exact explosive synchronization transitions in Kur…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
While considerable progress has been made in the analysis of large systems containing a single type of coupled dynamical component (e.g., coupled oscillators or coupled switches), systems containing diverse components (e.g., both…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…
The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than onedecade. Several frameworks have been proposed to…
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…
We investigate the dynamics of phase oscillators in the fully disordered Kuramoto model with couplings of defined asymmetry. The mean-field dynamics is reduced to a self-consistent stochastic single-oscillator problem which we analyze…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
In the context of the Kuramoto model of coupled oscillators with distributed natural frequencies interacting through a time-delayed mean-field, we derive as a function of the delay exact results for the stability boundary between the…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…
Synchronization in an array of mutually coupled systems with a finite time-delay in coupling is studied using Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…
We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the…
Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move…
What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated…