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Volume 32 Issue 03
Mar.  2006
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Journal of Beijing University of Aeronautics and Astronautics  > 2006  >  32(03): 320-323.
Wang Haixia, Lu Qishao. Some notes on complete synchronization of the coupled neurons[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(03): 320-323. (in Chinese)
Citation: Wang Haixia, Lu Qishao. Some notes on complete synchronization of the coupled neurons[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(03): 320-323. (in Chinese)
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Some notes on complete synchronization of the coupled neurons

  • School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

  • Received Date: 15 Jun 2005
  • Publish Date: 31 Mar 2006
    Abstract
  • Complete synchronization of two mutually coupled identical chaotic Hindmarsh-Rose neurons model with gap junction was studied. Gap junction isalso called electrical coupling, it acts as one of the main communications between neurons in nervous systems, its most important role is to make a large ensembles of neurons emit synchronous firing rhythm patterns.The traditional method to investigate complete synchronization was using numerical simulations, such as the conditional Lyapunov exponents, but it was lack of theoretical foundation and can only offer us a necessary condition to guarantee the occurrence of complete synchronization. Based on the conditional Lyapunov exponents method, synchronization of more coupled neurons is hard to be studied. So two new methods of Lyapunov function method and mode decomposition method here was introduced, and if and only if condition and the sufficient condition will be given. These methods are efficient to deal with more coupled neurons and nonsymmetrical coupling schemes, the validity of them was tested by numerical simulation.

     

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    • References(1)
  • [1] Pikovsky A, Rosenblum M, Kurths J. Synchronization, an universal concept in nonlinear sciences [M]. New York:Cambridge University Press, 2001 [2] Boccaletti S, Kurths J, Osipov G, %et al%. The synchronization of chaotic systems [J]. Physics Reports, 2002, 366:1~101 [3] Samuel B. Stability analysis for the synchronization of chaotic systems with different order:application to secure communications[J]. Phys Lett A, 2004, 326:102~113 [4] Wang Qingyun, Lu Qishao. Time delay-enhanced synchronization and regularization in two coupled chaotic neurons [J]. Chin Phys Lett, 2005,22(3):543~546 [5] Abarbanel H D I, Huerta R, Rabinovich M I. Synchronized action of synaptically coupled chaotic neurons Ⅰ:simulations using model neurons [J]. Neural Computation, 1996,8:1567~1602 [6] Ward T Oud, Ivan Tyukin. Sufficient condition for synchronization in an ensemble of Hindmarsh and rose neurons:passivity-based approach . 6th IFAC-Symposium on Nonlinear Control Systems . Stuttgart, 2004 [7] Lü Jinhu, Zhou Tianshou, Zhang Suochun. Chaos synchronization between linearly coupled chaotic systems [J]. Chaos, Solitons and Fractals, 2002,14:529~541 [8] Shi Xia, Lu Qishao. Firing patterns and complete synchronization of coupled hindmarsh-rose neurons[J]. Chin Phys, 2005,14:77~85
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