Bifurcation in two-dimensional neural network model with delay |
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| Authors: | Wei Jun-jie Zhang Chun-rui Li Xiu-ling |
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| Affiliation: | (1) Department of Mathematics, Harbin Institute of Technology, 150001 harbin, P.R. China;(2) Key Laboratory of Forestry Plant Ecology of Ministry of Education, Northeast Forestry University, 150040 Harbin, P.R. China;(3) Department of Basic Science and Art, Changchun Taxation College, 130022 Changchun, P.R. China |
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| Abstract: | A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory. Foundation item: the National Natural Science, Foundation of China (19831030) Biography: WEI Jun-jie, Professor, Doctor, E-mail: weijj@hit.edu.cn |
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| Keywords: | neural network centre manifold pitchfork bifurcation Hopf bifurcation |
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