Nonlinear analysis of dynamical complex networks

Copyright © 2013 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.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences

Controlled Hopwise Averaging: Bandwidth/Energy-Efficient Asynchronous Distributed Averaging for Wireless Networks

This paper addresses the problem of averaging numbers across a wireless network from an important, but largely neglected, viewpoint: bandwidth/energy efficiency. We show that existing distributed averaging schemes have several drawbacks and are inefficient, producing networked dynamical systems that evolve with wasteful communications. Motivated by this, we develop Controlled Hopwise Averaging (CHA), a distributed asynchronous algorithm that attempts to "make the most" out of each iteration by fully exploiting the broadcast nature of wireless medium and enabling control of when to initiate an iteration. We show that CHA admits a common quadratic Lyapunov function for analysis, derive bounds on its exponential convergence rate, and show that they outperform the convergence rate of Pairwise Averaging for some common graphs. We also introduce a new way to apply Lyapunov stability theory, using the Lyapunov function to perform greedy, decentralized, feedback iteration control. Finally, through extensive simulation on random geometric graphs, we show that CHA is substantially more efficient than several existing schemes, requiring far fewer transmissions to complete an averaging task.Comment: 33 pages, 4 figure

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Byzantine Attack and Defense in Cognitive Radio Networks: A Survey

The Byzantine attack in cooperative spectrum sensing (CSS), also known as the spectrum sensing data falsification (SSDF) attack in the literature, is one of the key adversaries to the success of cognitive radio networks (CRNs). In the past couple of years, the research on the Byzantine attack and defense strategies has gained worldwide increasing attention. In this paper, we provide a comprehensive survey and tutorial on the recent advances in the Byzantine attack and defense for CSS in CRNs. Specifically, we first briefly present the preliminaries of CSS for general readers, including signal detection techniques, hypothesis testing, and data fusion. Second, we analyze the spear and shield relation between Byzantine attack and defense from three aspects: the vulnerability of CSS to attack, the obstacles in CSS to defense, and the games between attack and defense. Then, we propose a taxonomy of the existing Byzantine attack behaviors and elaborate on the corresponding attack parameters, which determine where, who, how, and when to launch attacks. Next, from the perspectives of homogeneous or heterogeneous scenarios, we classify the existing defense algorithms, and provide an in-depth tutorial on the state-of-the-art Byzantine defense schemes, commonly known as robust or secure CSS in the literature. Furthermore, we highlight the unsolved research challenges and depict the future research directions.Comment: Accepted by IEEE Communications Surveys and Tutoiral