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Stability analysis of Hopfield neural networks with time delay. (English) Zbl 1015.92004
Summary: The global asymptotic stability for Hopfield neural networks with time delays is investigated. A theorem and two corollaries are obtained, where boundedness and differentiability assumptions in some other articles are avoided. Some sufficient conditions for existence of global asymptotic stable equilibria of the networks in this paper are better than the sufficient conditions in some other articles.

92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
Full Text: DOI
[1] LIANG Xue-bin, WU Li-de, Global exponential stability and application for Hopfield neural networks [J].Science in China (Series A), 1995,25(5):523--532. (in Chinese)
[2] Hopfield J J. Neurons with graded response have collective computational properties like those of two-state neurons [J].Proc Natl Acad Sci USA, 1984,81:3088--3092. · doi:10.1073/pnas.81.10.3088
[3] LIAO Xiao-feng, YU Jue-bang. Robust stability for interval Hopfield neural networks with time delay [J].IEEE Transacions on Neural Networks, 1998,9(5):1043--1045.
[4] CAO Jin-de, LI Ji-bin. The stability in neural networks with interneuronal transmission delays [J].Applied Mathematics and Mechanics (English Edition), 1998,19(5):457--462. · Zbl 0908.92003 · doi:10.1007/BF02457788
[5] HUANG Yong-min, ZHOU Dong-ming, CAO Jin-de. Convergence of a class of neural networks with delays [J].Journal of Biomathematics, 1998,13(1):47--49. (in Chinese)
[6] CAO Jin-de, LIN Yi-ping. Stability of a class of neural networks models with delay [J].Applied Mathematics and Mechanics (English Edition), 1999,20(8):912--916. · Zbl 0936.34063 · doi:10.1007/BF02452490
[7] CAO Jin-de, WAN Shi-dong. Global asymptotic stability of Hopfield neural networks with delays [J].Journal of Biomathematics, 1997,12(1):60--63. (in Chinese) · Zbl 0891.92001
[8] FANG Hui. The investigation of the periodic solutions and stability of many kinds of dynamic systems [D]. Ph. D. thesis, Chengdu, Sichuan University, Nov. 1999, 45--67.
[9] JIANG Yao-lin. LONG-time behavior of transmit solutions for cellular neural networks systems [J].Applied Mathematics and Mechanics (English Edition), 2000,21(3):321--326. · Zbl 0962.34040 · doi:10.1007/BF02459010
[10] LIAO Xiao-xin. The stability for Hopfield neural networks [J].Science in China (Series A), 1993,23(10):1032--1035.
[11] LIAO Xiao-xin.Theory Mathods and Application of Stability[M]. Wuhan: Huazhong University of Science and Technology Publishing House, 1999. (in Chinese)
[12] HU Shi-geng.Nonlinear Analysis and Methods[M]. Wuhan: Huzahong University of Science and technology Publshing House, 1996. (in Chinese).
[13] SHEN Yi, LIAO Xiao-xin. The dynamic analysis for generalized cellular neural networks with delay [J].Acta Electronoca Sinia, 1999,27(10):62--64. (in Chinese)
[14] Gopalsamy K.Stability and Oscillations in Dalay Differential Equations of Population Dynamics [M]. Netherlands: Dordrecht, Kluwer Academic Publishers, 1992. · Zbl 0752.34039
[15] LIAO Xiao-xin. Mathematical theory of cellular nural networks (II) [J].Science in China (Series A) 1994,24(10):1043--1046. (in Chinese)