Bifurcation in a Two-Dimensional Neural Network Model With Delay
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摘要: 研究了一类具时滞的二维神经网络模型.通过对该模型的特征方程根的分布分析, 在适当的参数平面上给出了分支图.得到了pitchfork分支曲线是一条直线,进而研究了每个平衡点的稳定性和Hopf分支的存在性.最后,利用规范性方法和中心流形理论,得到了Hopf分支的分支方向和分支周期界的稳定性.
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关键词:
- 神经网络 /
- 中心流形 /
- pitchfork分支 /
- Hopf分支
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.-
Key words:
- neural network /
- centre manifold /
- pitchfork bifurcation /
- Hopf bifurcation
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[1] Chen Y,Wu J.Slowly oscillating periodic solutions for a delayed frustrated network of two neurons [J].J Math Anal Appl,2001,259(1):188—208. doi: 10.1006/jmaa.2000.7410 [2] Wei J,Ruan S.Stability and bifurcation in a neural network model with two delays[J].Physica D,1999,130(3/4):255—272. doi: 10.1016/S0167-2789(99)00009-3 [3] Faria T.On a planar system modelling a neuron network with memory[J].J Differential Equations,2000,168(1):129—149. doi: 10.1006/jdeq.2000.3881 [4] Wei J,Velarde M,Makarov V.Oscillatory phenomena and stability of periodic solutions in a simple neural network with delay[J].Nonlinear Phenomena in Complex Systems,2002,5(4):407—417. [5] Wu J.Symmetric functional differential equations and neural networks with memory[J].Trans Amer Math Soc,1998,350(12):4799—4838. doi: 10.1090/S0002-9947-98-02083-2 [6] Wu J.Introduction to Neural Dynamics and Signal Transmission Delay[M].Berlin,New York:Walter de Gruyter,2001,120—150. [7] Babcock K L,Westervelt R M.Dynamics of simple electronic neural networks[J].Physica D,1987,28(4):305—359. doi: 10.1016/0167-2789(87)90021-2 [8] Hassard B D,Kazarinoff N D,Wan Y H.Theory and Applications of Hopf Bifurcation[M].Cambridge:Cambridge University Press,1981.
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