Related papers: Limitations and tradeoffs in synchronization of la…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
This brief paper further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive…
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…
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…
We consider performance deterioration of interconnected linear dynamical networks subject to exogenous stochastic disturbances. The focus of this paper is on first-order and second-order linear consensus networks. We employ the expected…
It has been recognized for quite some time that for some matrices the spectra are not enough to tell the complete story of the dynamics of the system, even for linear ODEs. While it is true that the eigenvalues control the asymptotic…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of…
In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
We study the synchronized interval in undirected and unweighted random networks of coupled oscillators as a function of the number of edges. In many coupled oscillator systems, synchronization is stable in a finite interval of coupling…
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…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
This paper gives a fresh look at network synchronization. Here we no longer analyze it from the view of mathematics, such as graph theory, while we probe into one from control theory. First, we analyze the synchronization region using the…
Scale-free networks are ubiquitous in social, biological and technological networked systems. Dynamic Scale-free networks and their synchronizations are important to understand and predict the behavior of social, biological and…
For the class of noisy time-delay linear consensus networks, we obtain explicit formulas for risk of large fluctuations of a scalar observable as a function of Laplacian spectrum and its eigenvectors. It is shown that there is an intrinsic…
We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the…
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…
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…
We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention in the interplay between networks topological disorder and its synchronization features. Firstly, we analyze…