Identifying the topology of a coupled Fitzhugh-Nagumo neurobiological network via a pinning mechanism

Authors:
Jin Zhou;Wenwu Yu;Xiumin Li;Michael Small;Jun-An Lu
Affiliations:
School of Mathematics and Statistics, Wuhan University, Wuhan, China and Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong;Department of Electronic Engineering, City University of Hong Kong, Hong Kong;Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong;Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong;School of Mathematics and Statistics, Wuhan University, Wuhan, China
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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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.