Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

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 that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Network synchronization: Spectral versus statistical properties

We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation, and clustering coefficient, can fail to characterize the synchronizability of networks

Phase Locking Induces Scale-Free Topologies in Networks of Coupled Oscillators

An initial unsynchronized ensemble of networking phase oscillators is further subjected to a growing process where a set of forcing oscillators, each one of them following the dynamics of a frequency pacemaker, are added to the pristine graph. Linking rules based on dynamical criteria are followed in the attachment process to force phase locking of the network with the external pacemaker. We show that the eventual locking occurs in correspondence to the arousal of a scale-free degree distribution in the original graph

Multi-agent Coordination in Directed Moving Neighborhood Random Networks

In this paper, we consider the consensus problem of dynamical multiple agents that communicate via a directed moving neighborhood random network. Each agent performs random walk on a weighted directed network. Agents interact with each other through random unidirectional information flow when they coincide in the underlying network at a given instant. For such a framework, we present sufficient conditions for almost sure asymptotic consensus. Some existed consensus schemes are shown to be reduced versions of the current model.Comment: 9 page

Incremental-dissipativity-based output synchronization of dynamical networks with switching topology

This paper studies asymptotic output synchronization for a class of dynamical networks with switching topology whose node dynamics are characterized by a quadratic form of incremental-dissipativity. The output synchronization problem of the switched network is first converted into a set stability analysis of a nonlinear dissipative system with a particular selection of input-output pair, which is related to special features of interconnected incremental-dissipative systems. Then, synchronization by designing switching among subnetworks, where none of them is self-synchronizing, is investigated by using the single Lyapunov function method. Algebraic synchronization criteria are established, and the results are applied to investigate synchronization of coupled biochemical oscillators. © 2014 IEEE.published_or_final_versio

Achieving synchronization in arrays of coupled differential systems with time-varying couplings

In this paper, we study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). The coupling considered here is time-varying in both the network structure and the reaction dynamics. Inspired by our previous paper [6], the extended Hajnal diameter is introduced and used to measure the synchronization in a general differential system. Then we find that the Hajnal diameter of the linear system induced by the time-varying coupling matrix and the largest Lyapunov exponent of the synchronized system play the key roles in synchronization analysis of LCODEs with the identity inner coupling matrix. As an application, we obtain a general sufficient condition guaranteeing directed time-varying graph to reach consensus. Example with numerical simulation is provided to show the effectiveness the theoretical results.Comment: 22 pages, 4 figure

Random walk on temporal networks with lasting edges

We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time of edges activation. We first propose a comprehensive analytical and numerical treatment on directed acyclic graphs. Once cycles are allowed in the network, non-Markovian trajectories may emerge, remarkably even if the walker and the evolution of the network edges are governed by memoryless Poisson processes. We then introduce a general analytical framework to characterize such non-Markovian walks and validate our findings with numerical simulations.Comment: 18 pages, 18 figure