147 research outputs found
Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs
We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results
Synchronization Analysis of Two Coupled Complex Networks with Time Delays
This paper studies the synchronized motions between two complex networks with time delays,
which include individual inner synchronization in each network and outer synchronization between
two networks. Based on the Lyapunov stability theory and the linear matrix equality (LMI), a
synchronous criterion for inner synchronization inside each network is derived. Numerical examples
are given which fit the theoretical analysis. In addition, the involved numerical results show that
the delays between two networks have little effect on inner synchronization. It is also shown that
synchronous motions within each network or between two networks are not enhanced if individual
intranetwork connections are allowed
Traffic congestion in interconnected complex networks
Traffic congestion in isolated complex networks has been investigated
extensively over the last decade. Coupled network models have recently been
developed to facilitate further understanding of real complex systems. Analysis
of traffic congestion in coupled complex networks, however, is still relatively
unexplored. In this paper, we try to explore the effect of interconnections on
traffic congestion in interconnected BA scale-free networks. We find that
assortative coupling can alleviate traffic congestion more readily than
disassortative and random coupling when the node processing capacity is
allocated based on node usage probability. Furthermore, the optimal coupling
probability can be found for assortative coupling. However, three types of
coupling preferences achieve similar traffic performance if all nodes share the
same processing capacity. We analyze interconnected Internet AS-level graphs of
South Korea and Japan and obtain similar results. Some practical suggestions
are presented to optimize such real-world interconnected networks accordingly.Comment: 8 page
Impulsive Synchronization of Nonlinearly Coupled Complex Networks
This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive interval. A numerical example is given to illustrate the effectiveness and feasibility of the proposed methods and results
Impulsive Synchronization of Nonlinearly Coupled Complex Networks
This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive interval. A numerical example is given to illustrate the effectiveness and feasibility of the proposed methods and results
Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control
We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations
Cluster synchronization of nonlinearly coupled complex networks via pinning control
Author name used in this publication: Francis AustinVersion of RecordPublishe
Synchronization Analysis of Two Coupled Complex Networks with Time Delays
This paper studies the synchronized motions between two complex networks with time delays, which include individual inner synchronization in each network and outer synchronization between two networks. Based on the Lyapunov stability theory and the linear matrix equality LMI , a synchronous criterion for inner synchronization inside each network is derived. Numerical examples are given which fit the theoretical analysis. In addition, the involved numerical results show that the delays between two networks have little effect on inner synchronization. It is also shown that synchronous motions within each network or between two networks are not enhanced if individual intranetwork connections are allowed
Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected].
By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the synchronization control problem is considered for two coupled discrete-time complex networks with time delays. The network under investigation is quite general to reflect the reality, where the state delays are allowed to be time varying with given lower and upper bounds, and the stochastic disturbances are assumed to be Brownian motions that affect not only the network coupling but also the overall networks. By utilizing the Lyapunov functional method combined with linear matrix inequality (LMI) techniques, we obtain several sufficient delay-dependent conditions that ensure the coupled networks to be globally exponentially synchronized in the mean square. A control law is designed to synchronize the addressed coupled complex networks in terms of certain LMIs that can be readily solved using the Matlab LMI toolbox. Two numerical examples are presented to show the validity of our theoretical analysis results.This work was supported by the Royal Society Sino-British Fellowship Trust Award of the
U.K
Mathematical problems for complex networks
Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy
is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
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