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具有任意激活函數(shù)的時(shí)延神經(jīng)元方程的Hopf分岔

周尚波,  廖曉峰,  虞厥邦

周尚波, 廖曉峰, 虞厥邦. 具有任意激活函數(shù)的時(shí)延神經(jīng)元方程的Hopf分岔[J]. 電子與信息學(xué)報(bào), 2002, 24(9): 1209-1217.
引用本文: 周尚波, 廖曉峰, 虞厥邦. 具有任意激活函數(shù)的時(shí)延神經(jīng)元方程的Hopf分岔[J]. 電子與信息學(xué)報(bào), 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.

具有任意激活函數(shù)的時(shí)延神經(jīng)元方程的Hopf分岔

Hopf bifurcation for delayed neuron equation with arbitrary activation function

  • 摘要: 該文研究了一個(gè)帶時(shí)延的神經(jīng)元方程,分析相應(yīng)的線性化方程的超越特征方程,研究了這個(gè)模型的線性穩(wěn)定性,對(duì)于神經(jīng)元來(lái)自過(guò)去狀態(tài)的抑制影響,作者發(fā)現(xiàn)當(dāng)這個(gè)影響值變化并通過(guò)一個(gè)臨界序列時(shí),這個(gè)模型會(huì)出現(xiàn)Hopf分岔,利用規(guī)范形式理論和中心流形定理,解析確定了周期解的穩(wěn)定性與Hopf分岔方向,數(shù)值例子也證實(shí)了所得結(jié)論。
    Abstract: In this paper, a neural equation with discrete time delay is studied, The transcendental equation corresponding to the above-mentioned linearized system is analyzed. The linear stability for this model has been investigated. For the case with inhibitory influence from the past state, it is found that Hopf bifurcation occurs when this influence varies and passes through a sequence of critical values. The stability of bifurcating periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Some numerical examples illustrated those results.
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  • 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]廖曉峰,吳中福,虞厥邦,帶分布時(shí)延神經(jīng)網(wǎng)絡(luò),從穩(wěn)定到振蕩再到穩(wěn)定的動(dòng)力學(xué)現(xiàn)象,電子科學(xué)學(xué)刊,2001,23(7),687-692.[6]王炎,廖曉峰,吳中福,虞厥邦,一個(gè)帶時(shí)延神經(jīng)網(wǎng)絡(luò)的分岔現(xiàn)象研究,電子科學(xué)學(xué)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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出版歷程
  • 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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