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Robust synchronization control of coupled chaotic neurons under external electrical stimulation. (English) Zbl 1197.37110
Summary: A robust adaptive neural network (NN) controller is proposed to realize the synchronization of two gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons under external electrical stimulation. Based on the Lyapunov stability theory, we derive the update laws of NN for approximating the nonlinear uncertain functions of the error dynamical system. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
37N25 Dynamical systems in biology
92C20 Neural biology
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[1] Pecora, L.M.; Carroll, T.L., Synchronization in chaotic systems, Phys rev lett, 64, 821-824, (1990) · Zbl 0938.37019
[2] Pecora, L.M.; Carroll, T.L.; Johnson, G.A.; Mar, D.J.; Heagy, J.F., Fundamentals of synchronization in chaotic systems, concepts, and applications, Chaos, 7, 520-543, (1997) · Zbl 0933.37030
[3] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D.L.; Zhou, C.S., The synchronization of chaotic systems, Phys rep, 366, 1, (2002) · Zbl 0995.37022
[4] Glass, L., Chaos in neural systems, (), 186-189
[5] Rabinovich, M.I.; Abarbanel, H.D.I., The role of chaos in neural systems, Neuroscience, 87, 1, 5-14, (1998)
[6] Chay, T.R., Chaos in a three-variable model of an excitable cell, Physica D, 16, 2, 233-242, (1985) · Zbl 0582.92007
[7] Gray, C.M.; König, P.; Engel, A.K.; Singer, W., Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties, Nature, 338, 334-337, (1989)
[8] Steriade, M.; McCormick, D.A.; Sejnowski, T.J., Halamocortical oscillations in the sleeping and aroused brain, Science, 262, 679-685, (1993)
[9] Roelfsema, P.R.; Engel, A.K.; König, P.; Singer, W., Visuomotor integration is associated with zero time-lag synchronization among cortical areas, Nature, 385, 157-161, (1997)
[10] Meister, M.; Wong, R.O.; Baylor, D.A.; Shatz, C.J., Synchronous bursts of action potentials in ganglion cells of the developing Mammalian retina, Science, 252, 939-943, (1991)
[11] Kreiter, A.K.; Singer, W., Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey, J neurosci, 16, 2381-2396, (1996)
[12] Harris-Warrick, RM., ()
[13] Rosa, M.L.; Rabinovich, M.I.; Huerta, R., Slow regularization through chaotic oscillation transfer in an unidirectional chain of hindmarsh – rose models, Phys lett A, 266, 88-93, (2000)
[14] Dhamala, M.; Jirsa, V.K.; Ding, M., Enhancement of neural synchrony by time delay, Phys rev lett, 92, 074104-1-074104-4, (2004)
[15] Wang, J.; Deng, B.; Tsang, K.M., Chaotic synchronization of neurons coupled with gap junction under external electrical stimulation, Chaos, solitons & fractals, 22, 469-476, (2004) · Zbl 1060.93525
[16] Wang, Q.Y.; Lu, Q.S.; Chen, G.R.; Guo, D.H., Chaos synchronization of coupled neurons with gap junctions, Phys lett A, 356, 17-25, (2006) · Zbl 1160.81304
[17] Elson, R.C.; Selverston, A.I.; Huerta, R.; Rulkov, N.F.; Rabinovich, M.I.; Abarbanel, H.D.I., Synchronous behavior of two coupled biological neurons, Phys rev lett, 81, 5692-5695, (1999)
[18] Cornejo-Pérez, O.; Femat, R., Unidirectional synchronization of hodgkik – huxley neurons, Chaos, solitons & fractals, 25, 43-53, (2005) · Zbl 1092.37539
[19] Wang, J.; Deng, B.; Fei, X.Y., Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control, Chaos, solitons & fractals, 29, 1, 182-189, (2006)
[20] Wang, J.; Deng, B.; Fei, X.Y., Chaotic synchronization of two coupled neurons via nonlinear control in external electrical stimulation, Chaos, solitons & fractals, 27, 5, 1272-1278, (2006) · Zbl 1092.92503
[21] Zhang, T.; Wang, J.; Fei, X.Y.; Deng, B., Synchronization of coupled fitzhugh – nagumo systems via MIMO feedback linearization control, Chaos, solitons & fractals, 33, 1, 194-202, (2007)
[22] Hodgkin, A.L.; Huxley, A.F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J physiol (London), 117, 500-544, (1952)
[23] Sanner, R.M.; Slotine, J.E., Gaussian networks for direct adaptive control, IEEE trans neural network, 3, 837-863, (1992)
[24] Gupta, M.M.; Rao, D.H., Neuro-control systems: theory and applications, (1994), IEEE Press New York
[25] Narendra, K.S.; Annaswamy, A.M., A new adaptive law for robust adaptation without persistent excitation, IEEE trans automat contr, AC-32, 134-145, (1987) · Zbl 0617.93035
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