Topology identification of complex dynamical networks

Abstract

Recently, some researchers investigated the topology identification for complex networks via LaSalle's invariance principle. The principle cannot be directly applied to time-varying systems since the positive limit sets are generally not invariant. In this paper, we study the topology identification problem for a class of weighted complex networks with time-varying node systems. Adaptive identification laws are proposed to estimate the coupling parameters of the networks with and without communication delays. We prove that the asymptotic identification is ensured by a persistently exciting condition. Numerical simulations are given to demonstrate the effectiveness of the proposed approach. © 2010 American Institute of Physics. ͓doi:10.1063/1.3421947͔The topology identification, as an inverse problem, is a significant issue in the study of complex networks. For example, if a major malfunction occurs in a communication network, power network, or the Internet, it is very important to quickly detect the location of the faulty line. This paper proposes a novel adaptive identification approach for the topology identification of the weighted complex dynamical networks. We show that the concept of persistent excitation plays a key role in the process of topology identification. Our result overcomes the limitation of previous methods, which rely on the use of LaSalle's invariance principle, and is applicable to networks with time-varying node systems and diverse time-varying coupling delays.

Topology Detection for Output‐Coupling Weighted Complex Dynamical Networks with Coupling and Transmission Delays

“…It provides positive possibility for future applications. However, in [21][22][23][24][25][26][27], information signals were assumed to be transmitted as instant communication between the drive and response systems, which is not practical enough. Due to long communication distance and unexpected transmission congestions, it definitely takes finite time for exchanging messages through the channel and the time delay should not be ignored.…”

“…The inner coupling matrix in [24] was chosen as a linear one. The topology detection problem for weighted timevarying dynamical networks with nonlinear inner coupling was addressed in [25]. Besides the topology detection, the estimation for uncertain system parameters [26] was conducted in general complex delayed dynamical networks [27].…”

“…Recently, the coupling delay has been taken into account for the more realistic topology detection [24][25][26][27] since it is ubiquitous in the interactions of network nodes. Sometimes it leads to additional complex dynamics [24].…”

“…Therefore, topology detection of complex dynamical networks [21][22][23][24][25][26][27][28][29] has become a significant topic for further studies. It is functionally powerful to employ the adaptive feedback control strategy to the structure detection of complex networks [21,22,[24][25][26][27][28]. The target topology matrix which Zhou and Lu [21] considered was not needed to be symmetric, irreducible, or diffusive.…”

湖南县域森林资源禀赋空间格局演变分析——一种空间网络模型的构建与验证

“…特性、 结构识别以及动力学行为特征等 [7][8][9] Table 2 Value of ecological influence degree of nature reserve/forest park ratio at all levels Table 3 The space network topological parameters of forest resources endowment in Hunan Abstract：Exploring spatial pattern evolution of forest resources has important theoretical and practical significance for forest resource sustainable development. Based on the degree of forest resource abundance，ecological impact and species abundance，the forest resource endowment degree of Hunan was evaluated in 1995， 2005 and 2015.…”