Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2012, Article ID 230980, 11 pages
http://dx.doi.org/10.1155/2012/230980
Research Article

Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

1Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Box 45650, Islamabad, Pakistan
2Department of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University, 30 Jangjeon-Dong, Geumjeong-Gu, Busan 609-735, Republic of Korea

Received 11 August 2012; Revised 3 October 2012; Accepted 3 October 2012

Academic Editor: Ricardo Femat

Copyright © 2012 Muhammad Rehan and Keum-Shik Hong. 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.

Linked References

  1. A. D. Garbo, M. Barbi, and S. Chillemi, “The synchronization properties of a network of inhibitory interneurons depend on the biophysical model,” BioSystems, vol. 88, no. 3, pp. 216–227, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. M. Aqil, K.-S. Hong, M.-Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage, vol. 63, no. 1, pp. 553–568, 2012. View at Google Scholar
  3. A. Alvarellos-González, A. Pazos, and A. B. Porto-Pazos, “Computational models of neuron-astrocyte interactions lead to improved efficacy in the performance of neural networks,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 476324, 10 pages, 2012. View at Google Scholar
  4. X.-S. Hu, K.-S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” Journal of Neural Engineering, vol. 9, no. 2, pp. 1–8, 2012. View at Google Scholar
  5. E. Kuriscak, P. Marsalek, J. Stroffek, and Z. Wünsch, “The effect of neural noise on spike time precision in a detailed CA3 neuron model,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 595398, 16 pages, 2012. View at Google Scholar
  6. L. H. Nguyen and K.-S. Hong, “Adaptive synchronization of two coupled chaotic Hindmarsh—Rose neurons by controlling the membrane potential of a slave neuron,” Applied Mathematical Modelling. In press. View at Publisher · View at Google Scholar
  7. R. Femat and G. Solís-Perales, “On the chaos synchronization phenomena,” Physics Letters A, vol. 262, no. 1, pp. 50–60, 1999. View at Google Scholar · View at Scopus
  8. O. Cornejo-Pérez and R. Femat, “Unidirectional synchronization of Hodgkin-Huxley neurons,” Chaos, Solitons and Fractals, vol. 25, no. 1, pp. 43–53, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. P. Limousin and I. M. Torres, “Deep brain stimulation for Parkinson's disease,” Neurotherapeutics, vol. 5, no. 2, pp. 309–319, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Jobst, “Brain stimulation for surgical epilepsy,” Epilepsy Research, vol. 89, no. 1, pp. 154–161, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. J. L. Ostrem and P. A. Starr, “Treatment of dystonia with deep brain stimulation,” Neurotherapeutics, vol. 5, no. 2, pp. 320–330, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. J. Wang, T. Zhang, and B. Deng, “Synchronization of FitzHugh-Nagumo neurons in external electrical stimulation via nonlinear control,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 30–38, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Zhang, J. Wang, X. Fei, and B. Deng, “Synchronization of coupled FitzHugh-Nagumo systems via MIMO feedback linearization control,” Chaos, Solitons and Fractals, vol. 33, no. 1, pp. 194–202, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Aqil, K.-S. Hong, and M. Y. Jeong, “Synchronization of coupled chaotic FitzHugh-Nagumo systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1615–1627, 2012. View at Google Scholar
  15. C. J. Thompson, D. C. Bardos, Y. S. Yang, and K. H. Joyner, “Nonlinear cable models for cells exposed to electric fields I. General theory and space-clamped solutions,” Chaos, solitons and fractals, vol. 10, no. 11, pp. 1825–1842, 1999. View at Publisher · View at Google Scholar · View at Scopus
  16. L. H. Nguyen and K.-S. Hong, “Synchronization of coupled chaotic FitzHugh-Nagumo neurons via Lyapunov functions,” Mathematics and Computers in Simulation, vol. 82, no. 4, pp. 590–603, 2011. View at Google Scholar
  17. J. Wang, B. Deng, and X. Fei, “Synchronization of chaotic neurons coupled with gap junction with time delays in external electrical stimulation,” Chaos, Solitons and Fractals, vol. 35, no. 3, pp. 512–518, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. N. Burić, K. Todorović, and N. Vasović, “Dynamics of noisy FitzHugh-Nagumo neurons with delayed coupling,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2405–2413, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Wang, “Pullback attractors for the non-autonomous FitzHugh-Nagumo system on unbounded domains,” Nonlinear Analysis, Theory, Methods and Applications, vol. 70, no. 11, pp. 3799–3815, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. D. Q. Wei, X. S. Luo, B. Zhang, and Y. H. Qin, “Controlling chaos in space-clamped FitzHugh-Nagumo neuron by adaptive passive method,” Nonlinear Analysis, vol. 11, no. 3, pp. 1752–1759, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Wang, Z. Zhang, and H. Li, “Synchronization of FitzHugh-Nagumo systems in EES via H∞ variable universe adaptive fuzzy control,” Chaos, Solitons and Fractals, vol. 36, no. 5, pp. 1332–1339, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. Y. Q. Che, J. Wang, S. S. Zhou, and B. Deng, “Robust synchronization control of coupled chaotic neurons under external electrical stimulation,” Chaos, Solitons and Fractals, vol. 40, no. 3, pp. 1333–1342, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Rehan and K.-S. Hong, “LMI-based robust adaptive synchronization of FitzHugh-Nagumo neurons with unknown parameters under uncertain external electrical stimulation,” Physics Letters A, vol. 375, no. 15, pp. 1666–1670, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Rehan, K.-S. Hong, and M. Aqil, “Synchronization of multiple chaotic FitzHugh-Nagumo neurons with gap junctions under external electrical stimulation,” Neurocomputing, vol. 74, no. 17, pp. 3296–3304, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. R. Femat, L. Kocarev, L. Van Gerven, and M. E. Monsivais-Pérez, “Towards generalized synchronization of strictly different chaotic systems,” Physics Letters A, vol. 342, no. 3, pp. 247–255, 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. J. G. B. Ramírez, K. P. C. Galarza, and R. Femat, “Generalized synchronization of strictly different systems: partial-state synchrony,” Chaos, Solitons & Fractals, vol. 45, no. 3, pp. 193–204, 2012. View at Google Scholar
  27. C. Wang and S. S. Ge, “Synchronization of two uncertain chaotic systems via adaptive backstepping,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 11, no. 6, pp. 1743–1751, 2001. View at Publisher · View at Google Scholar · View at Scopus
  28. C. Wang and S. S. Ge, “Adaptive synchronization of uncertain chaotic systems via backstepping design,” Chaos, solitons and fractals, vol. 12, no. 7, pp. 1199–1206, 2001. View at Publisher · View at Google Scholar · View at Scopus
  29. F. Blanchini, “The gain scheduling and the robust state feedback stabilization problems,” IEEE Transactions on Automatic Control, vol. 45, no. 11, pp. 2061–2070, 2000. View at Google Scholar · View at Scopus
  30. A. Iftar and U. Ozguner, “Local LQG/LTR controller design for decentralized systems,” IEEE Transactions on Automatic Control, vol. 32, no. 10, pp. 926–930, 1987. View at Google Scholar
  31. S. Skogestad and I. Postlethwaite, Multivariable Feedback Control Analysis and Design, John Wiley & Sons, England, UK, 2nd edition, 2005.
  32. G. Lu and D. W. C. Ho, “Full-order and reduced-order observers for Lipschitz descriptor systems: the unified LMI approach,” IEEE Transactions on Circuits and Systems II, vol. 53, no. 7, pp. 563–567, 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. E. Ruiz-Velázquez, R. Femat, and D. U. Campos-Delgado, “Blood glucose control for type I diabetes mellitus: a robust tracking H∞ problem,” Control Engineering Practice, vol. 12, no. 9, pp. 1179–1195, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. C. P. Flores-Gutiérrez, R. Femat, and E. Ruiz-Velázquez, “On hypoglycemic levels induced by H∞ control on type i diabetes mellitus,” Applied Mathematics and Computation, vol. 218, no. 2, pp. 376–385, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. M. Rehan, A. Ahmed, and N. Iqbal, “Static and low order anti-windup synthesis for cascade control systems with actuator saturation: an application to temperature-based process control,” ISA Transactions, vol. 49, no. 3, pp. 293–301, 2010. View at Publisher · View at Google Scholar · View at Scopus