一类简化的n个神经元时滞BAM神经网络模型的振动性

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1490-1501.

一类简化的n个神经元时滞BAM神经网络模型的振动性

冯春华

广西师范大学数学科学学院广西桂林 541004

收稿日期:2010-07-23 修回日期:2011-11-01 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
国家自然科学基金(10961005)资助

Oscillatory Behavior for a Simplified n-neuron BAM Neural Networks Model with Time Delays

FENG Chun-Hua

College of Mathematical Science, Guangxi Normal University, Guangxi Guilin 541004

Received:2010-07-23 Revised:2011-11-01 Online:2011-12-25 Published:2011-12-25
Supported by:
国家自然科学基金(10961005)资助

摘要/Abstract

摘要：

该文研究一类简化的n个神经元时滞BAM神经网络模型的振动性.利用Chafee的结论, 可以证明一类简化的n个神经元时滞BAM神经网络有唯一平衡点且不稳定. 这种特殊类型的不稳定性,结合系统所有解的有界性会迫使网络产生永久振动.得出此种振动行为产生的两个充分条件, 典型的数值仿真证明了理论结论的正确性.

关键词: n个神经元BAM神经网络, 时滞, 平衡点, 不稳定性, 振动性

Abstract:

In this paper, the existence of oscillations for a simplified n-neuron BAM neural network with time delays between neural interconnections is investigated. By using the Chafee's criterion, we prove that a simplified n-neuron BAM neural network has a unique equilibrium point which is unstable. This particular type of instability, combined with the boundedness of the solutions of the system, forces the network to generate a permanent oscillation. Two sufficient conditions for these oscillations are obtained. Typical simulation examples are presented.

Key words: n-neuron BAM neural network, Delay, Equilibrium point, Instability, Oscillation

中图分类号:

冯春华. 一类简化的n个神经元时滞BAM神经网络模型的振动性[J]. 数学物理学报, 2011, 31(6): 1490-1501.

FENG Chun-Hua. Oscillatory Behavior for a Simplified n-neuron BAM Neural Networks Model with Time Delays[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1490-1501.

参考文献

[1] B'elair J, Campbell S J, Driessche V D. Frustration, stability and delayinduced oscillations in a neural network model. SIAM J Appl Math, 1996, 56: 245--255

[2] Chafee N. A bifurcation problem for a functional differential equation of finitely retarded type. J Math Anal Appl, 1971, 35: 312--348

[3] Forti M, Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans, Circui Syst FTA, 1995, 42: 354--366

[4] Gao B, Zhang W N. Equilibria and their bifurcations in a recurrent neural network involving iterates of a transcendental function. IEEE Trans, NeuralNetworks, 2008, 19(5): 782--794

[5] Hale J. Theory of Functional Differential Equations. New York, Heidelberg, Berlin: Springer-Verlag, 1977

[6] Horn R, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 1985: 292--296

[7] Jin H L, Zacksenhouse M. Oscillatory neural networks for robotic yo-yo control. IEEE Trans, Neural Networks, 2003, 14: 317--325

[8] Li Y K. Global exponential stability of BAM neural networks with delays and impulses. Chaos, Solitons & Fractals, 2005, 24: 279--285

[9] Nishikawa T, Lai Y C, Hoppensteadt F C.Capacity of oscillatory associative memory networks with error-free retrieval. Physical Riview Lett, 2004, 92: 101--108

[10] Olien L, Béair J. Bifurcations, stability and monotonicity properties of a delayed neural network model. Physica D, 1997, 102: 349--363

[11] Ruiz A, Owens D H, Townley S. Existence, learning, and replication of periodic motion in recurrent neural networks. IEEE Trans Neural Networks, 1998, 9: 651--661

[12] Song Y L, Han M A, Wei J J. Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D, 2005, 200: 185--204

[13] Vidyasagar M. Nonlinear Systems Analysis. New Jersey: Prentice-Hall, 1978

[14] Wang Z S, Zhang H G, Yu W. Robust stability of Cohen- Grossberg neural networks via state transmission matrix. IEEE Trans Neural
Networks, 2009, 1: 69--174

[15] Xu J, Cao Y Y, Sun Y X, Tang J S. Absolute exponential stability of recurrent neural networks with generalized activation function. IEEE Trans Neural Networks, 2008, 19: 1075--1089

[16] Yu W, Cao J D. Stability and Holf bifurcations on a two-neuron system with time delay in the frequency domain. Int J Bifur Chaos, 2007, 17: 1355--1366

[17] 刘炳文, 黄立宏. 时滞细胞神经网络概周期解的存在性与全局指数稳定性. 数学物理学报, 2007, 27A(6): 1082--1088

[18] Yu W, Cao J D. Stability and Holf bifurcations analysison on a four-neuron BAM neural network with time delays. Phys Lett (A), 2007, 1: 64--78

[19] Yang Y, Ye J. Stability and bifurcation in a simplified five-neuron BAM neural network with delays. Chaos, Solitons & Fractals, 2009, 42: 2537--2563

[20] Yan X P, Li W T. Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays. Dis Dyn Nat Soc, 2006, 200: 1--29

[21] 赵洪涌,王广兰. 具有变时滞Hopfield神经网络的概周期解存在性与全局吸引性. 数学物理学报, 2004, 24A(6): 723--729

[22] Zhang H G, Wang Z S, Liu D R. Robust stability analysis for interval Cohen- Grossberg neural networks with unknown time-varying
delays. IEEE Trans Neural Networks, 2008, 19: 1942--1955

[23] Zhang C R, Zheng B D, Wang L C. Multiple Hopf bifurcations of symmetric BAM neural network with delay. Appl Math Lett, 2009, 22: 616--622

[24] 夏文华, 邓飞其, 罗毅平. 具周期输入的有限连续分布时滞神经网络周期解的全局指数稳定性. 数学物理学报, 2009, 29A(1): 171--178