A note on neural networks with multiple equilibrium points

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 43, Issue 6, 1996, Pages 487-491

  Forti, Mauro ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PIECEWISE LINEAR TECHNIQUES; VECTORS;

DEGREE THEORY; EQUILIBRIUM POINTS; NEURAL CIRCUITS; NEURON ACTIVATIONS;

CELLULAR NEURAL NETWORKS;

EID: 0030169001     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.503261     Document Type: Article

References (17)

1. I. W. Sandberg and A. N. Willson, Jr., "Some theorems on properties of dc equations of nonlinear networks," Bell Syst. Tech. J., vol. 48, pp. 1-34, 1969.
2. L. O. Chua and N. N. Wang, "On the application of degree theory to the analysis of resistive nonlinear networks," Int. J. Circuit Theory Applical, vol. 5, pp. 35-68, 1977.
3. T. Roska, "Some qualitative aspects of neural computing systems," in Pmc. 1988 IEEEISCAS, Helsinki, 1989, pp. 751-754.
4. D. Liu and A. N. Michel, "Asymptotic stability of systems operating on a closed hypercube," Syst. C'ontr. Lett., vol. 19, pp. 281-285. 1992.
5. M. Forti, S. Manetti, and M. Marini, "Necessary and sufficient condition for absolute stability of neural networks," IEEE Trans. Circuits Svst. I, vol. 41, pp. 491-494, 1994.
6. [fi] M. Forti, "On global asymptotic stability of a class of nonlinear systems arising in neural network theory," J. Differential Equations, vol. 113, no. 1, pp. 246 264, 1994.
7. E. Kaszkurewicz and A. Bhaya, "On a class of globally stable neural circuits," IEEE Trans. Circuits Syst. l vol. 41, pp. 171-174, 1994.
8. M. Forti and A. Tesi, "New conditions for global stability of neural networks with application to linear and quadratic programming problems," IEEE Trans. Circuits Syst. l, vol. 42, pp. 354-366, July 1995.
9. D. W. Tank and J. J. Hopfield. "Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming network," lEEETrans. Circuits Syst., vol. 33, pp. 533-541, 1986.
10. L. 0. Chua and L. Yang, "Cellular neural networks: Theory," IEEE Trans. Circuits Syst.. vol 35, pp. 1257-1272, 1988.
11. J. Li, A. N. Michel, and W. Porod, "Analysis and synthesis of a class of neural networks: Linear systems operating on a closed hypercube," IEEE Trans. Circuits Syst., vol. 36, pp. 1405-1422, 1989.
12. J. Cronin, Fixed Points and Topological Degree in Nonlinear Analysis. Providence, RI: Amer. Math. Soc., 1964.
13. M. M. Green and A. N. Willson, Jr., "(Almost) half of any circuit's operating points are unstable." IEEE Trans. Circuits Syst. I, vol. 41, pp. 286-293, 1994.
14. J. .1. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat. Acad. Sci., vol. 81, pp. 3088-3092, 1984.
15. L. O. Chua and T. Roska, "Stability of a class of nonreciprocal cellular neural networks," IEEE Trans. Circuits Syst., vol. 37, pp. 1520-1527, 1990.
16. D. Hershkowitz, "Recent directions in matrix stability," Linear Algebra Applical., vol. 171, pp. 161-186, 1992.
17. S. H. Bang, B. J. Sheu, and J. C.-F. Chang, "Search of optimal solutions in multi-level neural networks," in Proc. 1994 IEEE ISCAS. London, England, 1994, vol. 6, pp. 423-426.