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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.

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 [

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 [

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 [

The remainder of this paper is organized as follows. In Section

To demonstrate the topology identification of complex networks, in this paper, we consider a general complex dynamical network as in [

The coupling matrix

To identify the topology of the complex network, the following objective function is introduced as

Hence, the problem of topology identification is converted into that of a parameter optimization by the search of the minimal value of

In recent years, a swarm intelligent optimization algorithm called chaotic ant swam (CAS) algorithm is proposed to solve the optimization problem based on chaos theory [

The ants usually exchange information via certain direct or indirect communication methods. As a result of effective communication, the impact of the organization becomes stronger as time evolves. Finally, all the ants walk through the best path to forage food. Equation (

Based on the above discussions about the CAS algorithm, the detailed procedure for identifying the topology structure of a complex network is described as follows.

To identify the topology parameter of a complex network, some important parameters of the CAS algorithm should be firstly initialized. In this paper, the positive constant

Generate the initial position of the

By setting the initial time state vector

By setting the initial time state vector

Compute

Compute the value of objective function for each ant

Go to Step

In this section, we present several numerical simulation results to illustrate the effectiveness of the proposed method. Lorenz chaotic equation is taken as the node dynamical system of the

First of all, a nonsymmetric and non-synchronous diffusive network is considered, which includes three nodes with the topology matrix

Figure

(Color online) Estimation of nonsynchronous network topology showing the value

Estimation of nonsynchronous network topology showing the objective function value

In this example, a symmetric synchronous network is introduced to show the effectiveness of the proposed method. The parameters of the topology structure are set as

(Color online) Estimation of a synchronous network topology showing the value

We can see that the topology matrix

Comparison between two algorithms.

Algorithms | Objective value |
---|---|

CAS | 0.317 |

QPSO | 2.082 |

Estimation of nonsynchronous network topology showing the objective function value

In this paper, a topology identification method is proposed based on the CAS algorithm. The problem of topology identification is converted into that of parameter optimization. Compared with the constraints of identifying synchronous complex networks via adaptive feedback control method and the relatively poorer converging precision via QPSO-based topology identification method, the proposed method based on CAS algorithm can identify the topology structure of complex network effectively.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to thank the editor and all the anonymous reviewers for their helpful advice. This work is supported by the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (Grant no. 200951), the National Natural Science Foundation of China (Grant nos. 61170269, 61202362, and 61070209), the China Postdoctoral Science Foundation Funded Project (Grant no. 2013M540070), the Beijing Higher Education Young Elite Teacher Project, and the Asia Foresight Program under NSFC Grant (Grant no. 61161140320).