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Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

WeiYuan Zhang12* and JunMin Li1

Author Affiliations

1 School of Science, Xidian University, Shaan Xi Xi'an 710071, P.R. China

2 Institute of Maths and Applied Mathematics, Xianyang Normal University, Xianyang, ShaanXi 712000, P.R. China

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Boundary Value Problems 2012, 2012:2  doi:10.1186/1687-2770-2012-2

Published: 13 January 2012


In this article, a delay-differential equation modeling a bidirectional associative memory (BAM) neural networks (NNs) with reaction-diffusion terms is investigated. A feedback control law is derived to achieve the state global exponential synchronization of two identical BAM NNs with reaction-diffusion terms by constructing a suitable Lyapunov functional, using the drive-response approach and some inequality technique. A novel global exponential synchronization criterion is given in terms of inequalities, which can be checked easily. A numerical example is provided to demonstrate the effectiveness of the proposed results.

neural networks; reaction-diffusion; delays; global exponential synchronization; Lyapunov functional