On the asymptotic behavior of hopfield neural network with periodic inputs
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.
- Hopfield J J. Neural networks and physical system with emergent collective computational abilities [J].Proc Nat Academy Sci, 1982,79(4): 2554–2558. CrossRef
- Hopfield J J. Neurons with graded response have collective computational properties like those of two-state neurons[J].Proc Nat Academy Sci, 1984,81(5): 3088–3092. CrossRef
- LIAO Xiao-xin. Stability of Hopfield networks[J].Science in China Ser A, 1993,23(10): 1025–1035. (in Chinese)
- LIANG Xue-bin, WU Li-de. Global exponential stability of Hopfield networks and applications [J].Science in China Ser A, 1995,25(5): 523–532. (in Chinese)
- Guan Z H, Chen G. On the equilibria, stability and instability of Hopfield neural networks [J].IEEE Trans Neural Networks, 2000,11(2): 534–539. CrossRef
- LI Tie-cheng, WANG Duo. On the asymptotic behavior of a class artificial neural network with periodic input[J].JCU-Appl Math Ser A, 1997,12(1): 25–28. (in Chinese)
- HUANG Xian-kai. On the existence and stability of periodic solutions for Hopfield neural network equation with delay[J],Applied Mathematics and Mechnics (English Edition), 1999,20(10): 1116–1120.
- Gao J. Periodic oscillation and exponential stability of delayed CNN[J].Physics Letters A, 2000,270(3/4): 157–163.
- Gain R E, Mawhin J L.Coincidence Degree and Nonlinear Differential Equations [M].Lecture Note in Math,567, Berlin: Springer-Verlag, 1977, 40–41.
- Yoshizawa T.Stability Theory by Liapunov's Second Method[M]. Tokyo: The Math Soc of Japan, 1996, 165–169.
- On the asymptotic behavior of hopfield neural network with periodic inputs
Applied Mathematics and Mechanics
Volume 23, Issue 12 , pp 1367-1373
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Hopfield neural network
- periodic solution
- global exponential stability
- concidence degree
- Liapunov's function
- Industry Sectors
- Author Affiliations
- 1. Department of Physics, Hebei University of Technology, 300130, Tianjin, P R China
- 2. Department of Mathematics, Shanghai University, 200436, Shanghai, P R China
- 3. Naval Submarine Academy, 266071, Qingdao, P R China