Article

Identifying the Topology of a Coupled FitzHugh–Nagumo Neurobiological Network via a Pinning Mechanism

Sch. of Math. & Stat., Wuhan Univ., Wuhan, China
IEEE Transactions on Neural Networks (Impact Factor: 2.95). 11/2009; DOI: 10.1109/TNN.2009.2029102
Source: PubMed

ABSTRACT Topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology. Different from recent similar works in which the evolution of all the nodes in a complex network need to be received, this brief presents a novel criterion to identify the topology of a coupled FitzHugh-Nagumo (FHN) neurobiological network by receiving the membrane potentials of only a fraction of the neurons. Meanwhile, although incomplete information is received, the evolution of all the neurons including membrane potentials and recovery variables are traced. Based on Schur complement and Lyapunov stability theory, the exact weight configuration matrix can be estimated by a simple adaptive feedback control. The effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies.

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    ABSTRACT: The dynamics and function of a network are influenced by the topology of the network. A great need exists for the development of effective methods of inferring network structure. In the past few years, topology identification of complex networks has received intensive interest and quite a few works have been published in literature. However, in most of the publications, each state of a multidimensional node in the network has to be observable, and usually the nodal dynamics is assumed known. In this paper, a new method of recovering the underlying directed connections of a network from the observation of only one state of each node is proposed. The validity of the proposed approach is illustrated with a coupled FitzHugh-Nagumo neurobiological network by only observing the membrane potential of each neuron and found to outperform the traditional Granger causality method. The network coupling strength and noise intensity which might also affect the effectiveness of our method are further analyzed.
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