The Lojasiewicz exponent at an equilibrium point of a standard CNN IS 1/2

International Journal of Bifurcation and Chaos

Volumn 16, Issue 8, 2006, Pages 2191-2205

  Forti, Mauro ^a   Tesi, Alberto ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Cellular neural networks; Complete stability; Exponential convergence; Finite trajectory length; ojasiewicz inequality

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; VECTORS;

COMPLETE STABILITY; EXPONENTIAL CONVERGENCE; FINITE TRAJECTORY LENGTH; QUADRATIC FUNCTION; ŁOJASIEWICZ INEQUALITY;

CELLULAR NEURAL NETWORKS;

EID: 33750544696     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406016008     Document Type: Article

References (13)

1. Chua, L. O. & Yang, L. [1988] "Cellular neural networks: Theory," IEEE Trans. Circuits Syst. 35, 1257-1272.
2. Clarke, F. H. [1969] Optimization and Non-Smooth Analysis (John Wiley, NY).
3. Cygan, E., Krasinski, T. & Tworzewski, P. T. [1999] "Separation of algebraic sets and the Lojasiewicz exponent of polynomial mappings," Inv. Math. 136, 75-87.
4. Forti, M. & Tesi, A. [2001] "A new method to analyze complete stability of PWL cellular neural networks," Int. J. Bifurcation and Chaos 11, 655-676.
5. Forti, M. [2002] "Some extensions of a new method to analyze complete stability of neural networks," IEEE Trans. Neural Networks 13, 1230-1238.
6. Forti, M., Nistri, P. & Quincampoix, M. [2004] "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Trans. Circuits Syst.-I 51, 1741-1754.
7. Forti, M. & Tesi, A. [2004] "Absolute stability of analytic neural networks: An approach based on finite trajectory length," IEEE Trans. Circuits Syst.-I 51, 2460-2469.
8. Hale, J. & Koçak, H. [1991] Dynamics and Bifurcations (Springer-Verlag, NY).
9. Lancaster, P. & Tismenetsky, M. [1985] The Theory of Matrices, 2nd edition (Academic Press, Orlando).
10. Lojasiewicz, S. [1959] "Sur le problème de la division," 'Studia Math. T. XVIII, 87-136.
11. Łojasiewicz, S. [1965] "Ensembles semi-analytiques," I.H.E.S. notes.
12. Łojasiewicz, S. [1984] "Sur le trajectoires du gradient d'une fonction analytique," Seminari di Geometria 1982-1983, Università, di Bologna, Instituto di Geometria, Dipartimento di Matematica, pp. 115-117.
13. Palis, J. & De Mélo, W. [1982] Geometric Theory of Dynamical Systems (Springer-Verlag, Berlin).