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具有任意激活函数的时延神经元方程的Hopf分岔

周尚波 廖晓峰 虞厥邦

周尚波, 廖晓峰, 虞厥邦. 具有任意激活函数的时延神经元方程的Hopf分岔[J]. 电子与信息学报, 2002, 24(9): 1209-1217.
引用本文: 周尚波, 廖晓峰, 虞厥邦. 具有任意激活函数的时延神经元方程的Hopf分岔[J]. 电子与信息学报, 2002, 24(9): 1209-1217.
Zhou Shangbo, Liao Xiaofeng, Yu Juebang. Hopf bifurcation for delayed neuron equation with arbitrary activation function[J]. Journal of Electronics & Information Technology, 2002, 24(9): 1209-1217.
Citation: Zhou Shangbo, Liao Xiaofeng, Yu Juebang. Hopf bifurcation for delayed neuron equation with arbitrary activation function[J]. Journal of Electronics & Information Technology, 2002, 24(9): 1209-1217.

具有任意激活函数的时延神经元方程的Hopf分岔

Hopf bifurcation for delayed neuron equation with arbitrary activation function

  • 摘要: 该文研究了一个带时延的神经元方程,分析相应的线性化方程的超越特征方程,研究了这个模型的线性稳定性,对于神经元来自过去状态的抑制影响,作者发现当这个影响值变化并通过一个临界序列时,这个模型会出现Hopf分岔,利用规范形式理论和中心流形定理,解析确定了周期解的稳定性与Hopf分岔方向,数值例子也证实了所得结论。
  • K. Gopalsmy, I. Leung, Delay induced periodicity in a neural network of excitation and inhibition.[J].Physica D.1996,89:395-[2]K. Gopalsmay, Issic K. C. Leung, Convergence under dynamical thresholds with delays, IEEETrans. on Neural Networks, 1994, NN-8(2), 341-348.[3]L. Olien, J. Belair, Bifurcations, stability and monotonicity properties of a delayed neural networkmodel.[J]. Physica D.1997,102:349-[4]J. Belair, S. Dufour, Stability in a three-dimensional system of delay-differential equations, Can.Appl. Math. Quart., 1996, 4(2), 135-156.[5]廖晓峰,吴中福,虞厥邦,带分布时延神经网络,从稳定到振荡再到稳定的动力学现象,电子科学学刊,2001,23(7),687-692.[6]王炎,廖晓峰,吴中福,虞厥邦,一个带时延神经网络的分岔现象研究,电子科学学刊,2000,22(6),972-977.[7]Xiaofeng Liao, Zhongfu, Juebang Yu, Hopf bifurcation analysis of a neural system with a continuously distributed delay, International Symposium on Signal Processing and Intelligent System,Guangzhou, China, Nov. 1999. [8]Xiaofeng Liao, Zhongfu, Juebang Yu, Stability switches and bifurcation analysis of a neuralnetwork with continuously distributed delay, IEEE Trans. on SMC-I, 1999, SMC-I-29(6), 692-696.[8]Xiaofeng Liao, Kwok-wo Wong, Zhongfu Wu, Bifurcation analysis in a two-neuron system withcontinuously distributed delays, Accepted by Physical D, to appear. [10]K. Jack Hale, Sjoerd M. Verduyn Lunel, Introduction to Functional Differential Equations, NewYork, Springer-verlag, Inc., 1993.[9]B. D. Hassard, N. D. Kazarinoff, Y. H. Wan, Theory and Applications of Hopf Bifurcation,London, Cambridge, Univ, Press, 1981.
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出版历程
  • 收稿日期:  2000-06-29
  • 修回日期:  2000-12-21
  • 刊出日期:  2002-09-19

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