On the analysis of global and absolute stability of nonlinear continuous neural networks

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E80-A, Issue 1, 1997, Pages 223-228

  Liang, Xue Bin ^a,b   Yamaguchi, Toru ^a  

^a UTSUNOMIYA UNIVERSITY   (Japan)

^b FUDAN UNIVERSITY   (China)

Author keywords

Absolute stability; Equilibrium; Global asymptotic stability; Nonlinear continuous neural networks

Indexed keywords

ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; NONLINEAR NETWORK ANALYSIS;

GLOBAL ASYMPTOTIC STABILITY (GAS);

NEURAL NETWORKS;

EID: 0030653350     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. K. Sugawara, M. Harao, and S. Noguchi, "On the stability of equilibrium states of analogue neural networks," IEICE Trans., vol. J66-A, no. 3, pp. 258-265, 1983.
2. J. H. Li, A. N. Michel, and W. Porod, "Qualitative analysis and synthesis of a class of neural networks," IEEE Trans. Circuits & Syst., vol. 35, no. 8, pp. 976-986, 1988.
3. M. W. Hirsch, "Convergent activation dynamics in continuous time networks," Neural Networks, vol. 2, pp. 331-349, 1989.
4. D. G. Kelly, "Stability in contractive nonlinear neural networks," IEEE Trans. Biomed. Eng., vol. 37, no. 3, pp. 231-242, 1990.
5. F. M. A. Salam, Y. Wang, and M.-R. Choi, "On the analysis of dynamic feedback neural nets," IEEE Trans. Circuits & Syst., vol. 38, no. 2, pp. 196-201, 1991.
6. K. Matsuoka, "On absolute stability of neural networks," IEICE Trans., vol. J74-D-II, no. 4, pp. 536-542, 1991.
7. K. Matsuoka, "Stability conditions for nonlinear continuous neural networks with asymmetric connection weights," Neural Networks, vol. 5, pp. 495-500, 1992.
8. M. Forti, S. Manetti, and M. Marini, "A condition for global convergence of a class of symmetric neural circuits," IEEE Trans. Circuits & Syst. -I, vol. 39, no. 6, pp. 480-483, 1992.
9. E. Kaszkurewicz and A. Bhaya, "On a class of globally stable neural circuits," IEEE Trans. Circuits & Syst. -I, vol. 41, no. 2, pp. 171-174, 1994.
10. H. Yang and T. S. Dillon, "Exponential stability and oscillation of Hopfield graded response neural network," IEEE Trans. Neural Networks, vol. 5, no. 5, pp. 719-729, 1994.
11. J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat'1 Acad. Sci. U. S. A., vol. 81, pp. 3088-3092, 1984.
12. D. W. Tank and J. J. Hopfield, "Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming network," IEEE Trans. Circuits & Syst., vol. 33, no. 5, pp. 533-541, 1986.
13. M. P. Kennedy and L. O. Chua, "Neural networks for nonlinear programming," IEEE Trans. Circuits & Syst., vol. 35, no. 5, pp. 554-562, 1988.
14. A. Rodriguez-Vazquez, R. Dominguez-Castro, A. Rueda, and E. Sanchez-Sinencio, "Nonlinear switched-capacitor neural networks for optimization problems," IEEE Trans. Circuits & Syst., vol. 37, no. 3, pp. 384-398, 1990.
15. A. N. Michel and D. L. Gray, "Analysis and synthesis of neural networks with lower block triangular interconnecting structure," IEEE Trans. Circuits & Syst., vol. 37, no. 10, pp. 1267-1283, 1990.
16. G. Avitabile, M. Forti, S. Manetti, and M. Marini, "On a class of non-symmetric neural networks with applications to ADC," IEEE Trans. Circuits & Syst., vol. 38, no. 2, pp. 202-209, 1991.
17. M. Forti, S. Manetti, and M. Marini, "Necessary and sufficient condition for absolute stability of neural networks," IEEE Trans. Circuits & Syst. -I, vol. 41, no. 7, pp. 491-494, 1994.
18. E. Kaszkurewicz and A. Bhaya, "Comments on 'necessary and sufficient condition for absolute stability of neural networks'," IEEE Trans. Circuits & Syst.-I, vol. 42, no. 8, pp. 497-499, 1995.
19. M. Vidyasagar, "Nonlinear Systems Analysis," 2nd ed, Prentice-Hall, New Jersey, 1993.
20. A. N. Michel and R. K. Miller, "Qualitative Analysis of Large-Scale Dynamical Systems," Academic Press, New York, 1977.