Related papers: Reliability of Coupled Oscillators II: Larger Netw…
We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…
The desynchronization problems in oscillatory networks is considered. A new desynchronization notion is introduced and desynchronization conditions are provided. The desynchronization notion is formulated in terms of Yakubovich…
The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system…
The structure of a genetic network is uncovered by studying its response to external stimuli (input signals). We present a theory of propagation of an input signal through a linear stochastic genetic network. It is found that there are…
Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…
Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually…
Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags…
We investigate the stability of synchronization in networks of delay-coupled excitable neural oscillators. On the basis of the master stability function formalism, we demonstrate that synchronization is always stable for excitatory coupling…
We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…
We present a general approach to the study of synchrony in networks of weakly nonlinear systems described by singularly perturbed equations of the type $x''+x+\epsilon f(x,x')=0$. By performing a perturbative calculation based on normal…
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…
Coupled oscillator-based networks are an attractive approach for implementing hardware neural networks based on emerging nanotechnologies. However, the readout of the state of a coupled oscillator network is a difficult challenge in…
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The…
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…
We continue the investigation, started in [J. Stat. Phys. 166, 926-1015 (2017)], of a network of harmonic oscillators driven out of thermal equilibrium by heat reservoirs. We study the statistics of the fluctuations of the heat fluxes…
We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies.…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…