Repeated-drive adaptive feedback identification of network topologies

Abstract

The identification of the topological structures of complex networks from dynamical information is a significant inverse problem. How to infer the information of network topology from short-time dynamical data is a challenging topic. The presence of synchronization among nodes makes the identification of network topology difficult. In this paper we present an efficient method called the repeated-drive adaptive feedback scheme to reveal the network connectivity from short-time dynamics. By applying the short asynchronous transient data as a repeated drive, the adjacency matrix can be successfully determined in terms of the modified adaptive feedback scheme. This improved scheme is valid for both synchronous and asynchronous cases of the network and is especially efficient in the presence of global or local synchronization, where the transient drive can be obtained by perturbing the system to get a very short asynchronous transient. The detection speed of our scheme exhibits the optimized effect by adjusting the time-series segment length and the coupling strength among nodes in the network.

Topology and parameters recognition of uncertain complex networks via nonidentical adaptive synchronization

“…Example 2 For the system (15) and (16) 3,28), we consider there are five nodes in each network, and let the coupling configuration matrix as The error evolution curves of three states and the control strength k i (i = 1, . .…”

“…In this regard, the generalized outer synchronization was proposed in [27] to figure out this kind of issues. Although topology structure and coupling strengths were recognized in [28,29] through the outer synchronization by constructing a response network, the requirements for this kind of issues are strict, such that the dimension of each system in two networks should be identical. It should be noted that the restriction limits the range of application in recognizing system parameters and topology structures.…”

Consistency between functional and structural networks of coupled nonlinear oscillators

“…There are in fact circumstances in which the functional connections can be established between units without direct physical connections [6], leading to phenomena such as partial * Email address:wangxg@snnu.edu.cn synchronization [7], noise-induced coherence [8], generalized and driven synchronization [9], etc. The nontrivial interplay between structural and functional connectivities raises a challenging question: how to infer the physical connections from the measured data of dynamical activities, referred to as the inverse problem in complex systems [10][11][12][13][14][15][16][17].…”

“…Networks of coupled nonlinear oscillators serve as a paradigmatic model to address the inverse problem. The past decade has witnessed a great deal of progress in this area of research [11][12][13][14][15][16][17][18][19][20][21][22][23]. In a general setting, an ensemble of nonlinear oscillators (nodes) are coupled through a complicated pattern, giving rise to various collective behaviors at the system level.…”