Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Mathematical Problems in Engineering, Oct 2013

Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.

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Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm Haipeng Peng,1 Lixiang Li,1 Jürgen Kurths,2 Shudong Li,3 and Yixian Yang1,4 1Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China 2Potsdam Institute for Climate Impact Research, D14473 Potsdam, Germany 3College of Mathematics, Shandong Institute of Business and Technology, Yantai, Shandong 264005, China 4National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China Received 18 July 2013; Accepted 22 August 2013 Academic Editor: Ming Li Copyright © 2013 Haipeng Peng 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. Abstract Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method. 1. Introduction So far, most researches on complex networks are based on their exact structure dynamics. However, there is often various unknown or uncertain information in complex networks of the real world. This information including the topology connection of networks, and dynamical parameters of nodes, is always partially known and also changes continuously in many real complex networks such as gene networks, protein-DNA structure network, power grid networks, and biological neural networks [1–4]. Knowledge about the identification of the topology of complex networks is the prerequisite to analyze, control, and predict their dynamical behaviors. Therefore, this topic has drawn great attention of many researchers, since it is of great theoretical and practical significance to use the dynamics of observed nodes for the identification of the network structure [5–7]. The problem of topology identification can be formulated as a gray box model. From this viewpoint, a basic mathematical model of the topology for the complex network can be constructed, although its exact structure peculiarities are not entirely known. In the model of a complex network, there are often some unknown structure parameters which can be completed via topology identification. Therefore, if the basic mathematical model of its topological structure is built, then we only need to identify the unknown structure parameters of this network. Recently, some research on topology identification of complex networks has emerged to identify some complex networks and some time-delay networks [8]. These researchers mainly used an adaptive feedback control algorithm to solve the problem of topological identification. But this algorithm may fail if the network is in a synchronous regime. In [9], an improved adaptive feedback control method was proposed to make it identifiable in synchronous complex networks. However, this improved method should change the coupling mode of its topology. In addition, to adapt this improved adaptive feedback control method, the dynamical parameter of each node must be observable, which is especially difficult to realize in most real networks such as metabolic networks and power grid networks. In this paper, a method of topology identification for complex networks is proposed which is based on a chaotic ant swarm (CAS) algorithm. The problem of topology identification is converted into that of parameter optimization which could be solved by the CAS optimization algorithm [10]. The CAS algorithm was inspired by biological experiments of single ant’s chaotic behavior. This CAS method is different from those of ant colony optimization (ACO), since the CAS algorithm combines chaotic and self-organizing behaviors of ants with the advantages of swarm-based algorithms. The CAS algorithm is a global optimization algorithm, and it can deal with topology identification of complex networks effectively when they are in a nonsynchronous and even when they are in a synchronous regime. The remainder of this paper is organized as follows. In Section 2, the problem formulation of topology identification for complex networks is presented. In Section 3, the chaotic ant swarm algorithm is introduced. In Section 4, results of numerical simulations are given. F (...truncated)


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Haipeng Peng, Lixiang Li, Jürgen Kurths, Shudong Li, Yixian Yang. Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm, Mathematical Problems in Engineering, 2013, 2013, DOI: 10.1155/2013/401983