Qualitative Analysis of Neural Networks

IEEE Transactions on Circuits and Systems

Volumn 36, Issue 2, 1989, Pages 229-243

  Michel, Anthony N ^a   Farrell, Jay A ^b   Porod, Wolfgang ^b  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

SYSTEM STABILITY--LYAPUNOV METHODS;

ASYMPTOTIC STABILITY; EXPONENTIAL STABILITY; HOPFIELD MODEL; LARGE-SCALE INTERCONNECTED DYNAMICAL SYSTEMS; NEURAL NETWORKS;

SYSTEMS SCIENCE AND CYBERNETICS;

EID: 0024610496     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/31.20200     Document Type: Article

References (21)

1. J. J. Hopfield and D. W. Tank, “Computing with neural circuits: A model,” Science, vol. 233, pp. 625-633, 1986.
2. Neural Networks for Computing, American Institute of Physics Conf. 151, John S. Denker, Ed., Snowbird, UT, 1986.
3. J. A. Anderson, “Cognition and psychological computation with neural models,” IEEE Trans. Syst., Man, Cybern., vol. SMC-13, pp. 799-815, 1983.
4. G. E. Hinton and J. A. Anderson, Eds., Parallel Models of Associative Memory, Erlbaum, 1981.
5. T. Kohonen, Self-Organization and Associative Memory. New York: Springer-Verlag, 1984.
6. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” in Proc. Natl. Acad. Sci. U.S.A., vol. 79, pp. 2554-2558, 1982.
7. “Neurons with graded response have collective computational properties like those of two-state neurons,” in Proc. Natl. Acad. Sci. U.S.A., vol. 81, pp. 3088-3092, 1984.
8. D. W. Tank and J. J. Hopfield, “Simple ‘neural’ optimization networks: A/D converter, signal decision circuit, and a linear programming circuit,” IEEE Trans. Circuits Syst., vol. CAS-32, pp. 533-541, 1986.
9. G. A. Carpenter, M. A. Cohen, and S. Grossberg, “ Computing with neural networks,” Science, vol. 235, pp. 1226-1227, 1987.
10. E. G. Goles and G. Vichniac, the American Inst. Phys. Conf. on Neural Networks for Computing, Snowbird, UT, pp. 165-181, 1986.
11. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems. New York: Academic, 1977.
12. R. K. Miller and A. N. Michel, Ordinary Differential Equations. New York: Academic, 1982.
13. A. N. Michel, “ On the status of stability of interconnected systems,” IEEE Trans. Automat. Contr., vol. AC-28, pp. 639-653, June 1983.
14. M. A. Pai, Power System Stability. Amsterdam, The Netherlands: North Holland, 1981.
15. A. N. Michel, N. R. Sarabudla, and R. K. Miller, “Stability analysis of complex dynamical systems: Some computational methods,” Circuits, Systems and Signal Processing, vol. 1, no. 2, pp. 171-202, 1982.
16. L. J. T. Grujic, A. A. Martynyuk, and M. Ribbens-Pavella, Stability of Large-Scale Systems Under Structural and Singular Perturbations, Nauka Dumka, Kiev, USSR, 1984.
17. I. W. Sandberg, “Some theorems on dynamic response of nonlinear transistor networks,” Bell Syst. Tech. J., vol. 48, pp. 35-54, 1969.
18. J. J. Hopfield and D. W. Tank, “Neural computation of decision in optimization problems,” Biol. Cybern., vol. 52, pp. 398-412, 1985.
19. M. A. Cohen, “Absolute stability of global pattern formulation and parallel memory storage by competitive neural networks,” IEEE Trans. Syst. Man, Cybern., vol. 13, pp. 815-826, 1983.
20. M. P. Kennedy and L. O. Chua, “Neural networks for nonlinear programming,” presented at the IEEE First Ann. Int. Conf. on Neural Networks, San Diego, CA, June 21-24, 1987.
21. 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, pp. 976-986, Aug. 1988.