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Mathematical Problems in Engineering
Volume 2017, Article ID 7587294, 10 pages
https://doi.org/10.1155/2017/7587294
Research Article

Robust Master-Slave Synchronization of Neuronal Systems

1División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana Azcapotzalco, Ciudad de México, Mexico
2Facultad de Ciencias Químicas, Universidad Veracruzana, Campus Xalapa, Xalapa, VER, Mexico
3Cátedras CONACyT, Universidad Autónoma Metropolitana Azcapotzalco, Ciudad de México, Mexico

Correspondence should be addressed to Hector Puebla; xm.mau.cza.oerroc@albeuph

Received 27 August 2017; Revised 4 December 2017; Accepted 11 December 2017; Published 28 December 2017

Academic Editor: Miguel A. F. Sanjuan

Copyright © 2017 Hector Puebla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The desire to understand physiological mechanisms of neuronal systems has led to the introduction of engineering concepts to explain how the brain works. The synchronization of neurons is a central topic in understanding the behavior of living organisms in neurosciences and has been addressed using concepts from control engineering. We introduce a simple and reliable robust synchronization approach for neuronal systems. The proposed synchronization method is based on a master-slave configuration in conjunction with a coupling input enhanced with compensation of model uncertainties. Our approach has two nice features for the synchronization of neuronal systems: (i) a simple structure that uses the minimum information and (ii) good robustness properties against model uncertainties and noise. Two benchmark neuronal systems, Hodgkin-Huxley and Hindmarsh-Rose neurons, are used to illustrate our findings. The proposed synchronization approach is aimed at gaining insight into the effect of external electrical stimulation of nerve cells.