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We study synchronization in scalar nonlinear systems connected over a linear network with stochastic uncertainty in their interactions. We provide a sufficient condition for the synchronization of such network systems expressed in terms of…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
In this paper, we investigate synchronization in a small-world network of coupled nonlinear oscillators. This network is constructed by introducing random shortcuts in a nearest-neighbors ring. The local stability of the synchronous state…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two…
We study the synchronization of fully-connected and totally excitatory integrate and fire neural networks in presence of Gaussian white noises. Using a large deviation principle, we prove the stability of the synchronized state under…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…
We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. Using the known exact threshold value from the theory of differential equations with delays, we provide the…
Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the…
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
It is well-known that the synchronization of diffusively-coupled systems on networks strongly depends on the network topology. In particular, the so-called algebraic connectivity $\mu_{N-1}$, or the smallest non-zero eigenvalue of the…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…