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State-Dependent Impulsive Neural Networks

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Modeling, Dynamics, Optimization and Bioeconomics II (DGS 2014)

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Abstract

In this chapter, we address a new model of neural networks related to the discontinuity phenomena which is called state-dependent impulsive neural networks. By means of B-equivalence method, we reduce these networks to a fix time impulsive neural networks system. In the first part of this study, sufficient conditions for existence and uniqueness of exponentially stable almost periodic solution for recurrent neural networks are investigated. In the second part, sufficient conditions ensuring the existence, uniqueness and global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks are obtained by employing an appropriate Lyapunov function and linear matrix inequality (LMI). Finally, an illustrative example is given to show the effectiveness of the theoretical results.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Mustafa Şaylı

  2. College of Computing and Digital Media, School of Computing, DePaul University, 243 S Wabash Ave, Chicago, IL, 60604, USA

    Enes Yılmaz

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  1. Mustafa Şaylı
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  2. Enes Yılmaz
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Correspondence to Enes Yılmaz .

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Editors and Affiliations

  1. Department of Mathematics and LIAAD-INESC TEC, University of Porto, Porto, Portugal

    Alberto A. Pinto

  2. Department of Agricultural and Resource Economics, University of California, Berkeley, California, USA

    David Zilberman

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Şaylı, M., Yılmaz, E. (2017). State-Dependent Impulsive Neural Networks. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics II. DGS 2014. Springer Proceedings in Mathematics & Statistics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-55236-1_19

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