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Volume 24 Issue 9
Sep.  2002
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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.

Hopf bifurcation for delayed neuron equation with arbitrary activation function

  • Received Date: 2000-06-29
  • Rev Recd Date: 2000-12-21
  • Publish Date: 2002-09-19
  • 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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