Related papers: Synchronization, Consensus of Complex Networks and…
This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. The methods commonly used to study cluster synchronization in networks of coupled oscillators ground on simplifying…
Determining conditions on the coupling strength for the synchronization in networks of interconnected oscillators is a challenging problem in nonlinear dynamics. While sophisticated mathematical methods have been used to derive conditions,…
We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough…
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…
The famous Fischer, Lynch, and Paterson impossibility proof shows that it is impossible to solve the consensus problem in a natural model of an asynchronous distributed system if even a single process can fail. Since its publication, two…
In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the…
We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [5]. We also briefly discuss sufficient conditions for…
We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the…
In this contribution, we establish a model for multichannel cognitive radio networks (CRNs) using the theory of priority queues. This model enables us to conduct a performance analysis in the most general form by the derivation of the…
We study under which conditions systems of coupled oscillators on complex networks display remote synchronization, a situation where pairs of vertices, not necessarily physically linked, but with the same network symmetry, are synchronized.
With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most of these previous…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…
Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the entropy by the…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…