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三元环状神经网络的稳定性 被引量：3

Stability of a Ring Neural Network with Delays
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摘要 该文针对一个带自反馈的多时滞环状神经网络系统,在整个参数空间中,分区域系统完整地讨论了系统平凡解稳定与不稳定的条件,并根据正实部特征根个数依参数变动的变化规律,给出了不同参数条件下平凡解的相应最大稳定区域边界,改进和完善了先前的结果. A system of ring neural network with self-feedback and multiple delays is considered. Conditions for the stability and unstability of the trivial solution of this system are completely represented in a parameter space.According to the regulation of the variation of the number of eigenvalues with positive real parts,for different parameters,the authors investigate the boundary of the largest stability set,improve and complete the former conclusions.
作者 邹劭芬 王耀南 黄立宏
机构地区 湖南大学数学与计量经济学院 湖南大学电气与信息工程学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2010年第6期1654-1665,共12页 Acta Mathematica Scientia
基金 湖南省博士后基金(2009RS3004) 国家自然科学基金(60775047 10771055 60835004) 国家863项目(2007AA04Z244)资助
关键词 神经网络 时滞 线性稳定性 最大稳定区域 Neural network Delay Linear stability Largest stability set
分类号 O175.13 [理学—基础数学]
  • 相关文献

参考文献18

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二级参考文献17

  • 1Hopfield J J. Neurons with Graded Response have Collective Computational Properties Like Those of Two-state Neurons. Proc. Natl. Acad. Sci. USA, 1984, 81:3088-3092
  • 2Anderson P, Gross O, Lomo T et al. Participation of Inhibitory Interneruons in the Control of Hippocampal Cortical Output. In: The Interneuron (M. Brazier Ed.) Los Angeles: University of California Press, 1969
  • 3Eccles J C, Ito M, Szenfagothai J. The Cerebellum as Neuronal Machine. New York: Springer-Verlag, 1967
  • 4Szenfagothai J. The "module-concept" in Cerebral Cortex Architecture. Brain Research, 1967, 95: 475-496
  • 5Pakdaman K, Grotta-Ragazzo C, Malta C P, Arino O, Vibert J-F. Transient Oscillations in Continuoustime Excitatory Ring Neural Networks with Delay. Physical Review E, 1997, 55:3234-3247
  • 6Othmer H G, Scriven L E. Instability and Dynamics Pattern in Cellular Networks. J. Theoret. Biol., 1971, 32:507-537
  • 7Smale S. A Mathematical Model of Two Cells via Turing's Equation. In: Some Mathematical Questions in Biology V (J.D. Cowan, Ed). AMS Lecture Notes on Mathematics in the Life Science, 1974, 6, 15-26
  • 8Howard L. Nonlinear Oscillations in Biology (F.R. Hopp ensteadt, Ed). AMS, Lecture Notes in Applied Mathematics, 1979, 17. 1-69
  • 9Shayer L P, Campbell S A. Stability, Bifurcation and Multistability in a System of Two Coupled Neurons with Multiple Time Delays. SIAM J. Appl. Math., 2000, 61:673-700
  • 10Huang L, Wu J. Nonlinear Waves in Networks of Neurons with Delayed Feedback: Pattern Formation and Continuation. SIAM J. Math. Anal., 2003, 34(4): 836-860

共引文献4

同被引文献13

  • 1邹劭芬,黄立宏.多时滞环状神经网络的稳定性[J].应用数学学报,2007,30(4):707-718. 被引量：5
  • 2Pakdaman K, Malta P C, Grotta-Ragazzo C , et al. Transient Oscillations in Continuous Time Excitatory Ring Neural Networks with Delay[ J]. Physcial Review E, 1997,55:3234-3247.
  • 3Wei Junjie, Yuan Yuan. Synchronized Hopf Bifurcation Analysis in A Neural Network Model with Delays [ J ]. J Math Anal Appl, 2005,312: 205-229.
  • 4Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics [ M ]. Dordrecbt: Kluwer Academic, 1992:66-78.
  • 5Li Xiaodi, Fu Xilin, Balasubramaniam P, et al. Existence, Uniqueness and Stability Analysis of Recurrent Neural Networks with Time Delay in the Leakage Term Under Impulsive [ J]. Nonlinear Analysis: Real.World Applications, 2010, 11: 4092-4108.
  • 6Wang Linshan , Xu Daoyi. Asymptotic Behavior of A Class of Reaction-diffusion Equations with Delays [ J ]. J Math Anal Appl, 2003,281:439 -453.
  • 7Zhao Hongyong, Wang Kunlun. Dynamical Behaviors of Cohen-Grossberg Neural Networks with Delays and Reaction- diffusion Terms [ J ]. Neurocomputing, 2006,70:536-543.
  • 8徐旭,张洁,梁艳春.小世界联接对神经网络稳定性的影响[J].吉林大学学报（理学版）,2008,46(5):873-876. 被引量：4
  • 9盛洁波,曹爱华,李建军.一类三元环状神经网络周期解的存在性[J].江西理工大学学报,2008,29(6):41-45. 被引量：1
  • 10廖晓昕,杨叔子,程时杰,沈轶.具有反应扩散的广义神经网络的稳定性[J].中国科学（E辑）,2002,32(1):87-94. 被引量：23

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数学物理学报（A辑）
2010年 第6期

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