Exponential Convergence for HCNNs with Oscillating Coefficients in Leakage Terms

详细信息    查看全文

• 作者：Ani Jiang
• 关键词：High ; order cellular neural network ; Exponential convergence ; Oscillating coefficient ; Leakage term ; 34C25 ; 34D40
• 刊名：Neural Processing Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：43
• 期：1
• 页码：285-294
• 全文大小：414 KB
• 参考文献：1.Dembo A, Farotimi O, Kailath T (1991) High-order absolutely stable neural networks. IEEE Trans Circuits Syst 38:57–65CrossRef
  2.Psaltis D, Park CH, Hong J (1988) Higher order associative memories and their optical implementations. Neural Netw 1:143–163CrossRef
  3.Karayiannis NB, Venetsanopoulos AN (1995) On the training and performance of high-order neural networks. Math Biosci 129(2):143–168CrossRef
  4.Huang Z, Peng L, Xu M (2010) Anti-periodic solutions for high-order cellular neural networks with time-varying delays. Electron J Differ Equ 59:1–9
  5.Ou CX (2008) Anti-periodic solutions for high-order Hopfield neural networks. Comput Math Appl 56(7):1838–1844MathSciNet CrossRef
  6.Duan L, Huang L, Guo Z (2014) Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations. Nonlinear Dyn. doi:10.​1007/​s11071-014-1392-3
  7.Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325:1117–1132MathSciNet CrossRef
  8.Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal 14:559–C566CrossRef
  9.Chen Z, Yang M (2013) Exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Comput Appl 23:2221–2229CrossRef
  10.Yu Y, Jiao W (2014) New results on exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Process Lett 39:167–177CrossRef
  11.Yi X, Shao J, Yu Y, Xiao B (2008) New convergence behavior of high-order Hopfield neural networks with time-varying coefficients. J Comput Appl Math 219:216–222MathSciNet CrossRef
  12.Zhang H, Wang W, Xiao B (2011) Exponential convergence for high-order recurrent neural networks with a class of general activation functions. Appl Math Model 35:123–129MathSciNet CrossRef
  13.Zhang A (2013) Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays. Adv Differ Equ 162:1–14
  14.Jia R, Yang M (2014) Convergence for HRNNs with unbounded activation functions and time-varying delays in the leakage terms. Neural Process Lett 39:69–79CrossRef
  15.Xiong W (2014) New result on convergence for HCNNs with time-varying leakage delays. Neural Comput Appl. doi:10.​1007/​s00521-014-1733-7
  16.Berezansky L, Braverman E (2009) On exponential stability of a linear delay differential equation with an oscillating coefficient. Appl Math Lett 22:1833–1837MathSciNet CrossRef
  
• 作者单位：Ani Jiang (1)
  
  1. College of Mathematics and Computational Science, Hunan University of Arts and Science, Changde, 415000, Hunan, People’s Republic of China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Complexity
  Artificial Intelligence and Robotics
  Electronic and Computer Engineering
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-773X

文摘

The paper is concerned with the exponential convergence for a class of high-order cellular neural networks with oscillating coefficients in leakage terms. By employing the differential inequality techniques, we establish a novel result to ensure that all solutions of the addressed system converge exponentially to zero vector. Our approach handles particular cases which were not considered in some early relevant results. An example along with its numerical simulation is presented to demonstrate the validity of the proposed result. Keywords High-order cellular neural network Exponential convergence Oscillating coefficient Leakage term