Robust global exponential stability of Cohen-Grossberg neural networks with time delays

IEEE Transactions on Neural Networks

Volumn 15, Issue 1, 2004, Pages 203-205

  Chen, Tianping ^a   Rong, Libin ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Global exponential convergence; M matrix; Neural networks; Stability; Time delay

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); MATHEMATICAL MODELS; MATRIX ALGEBRA; THEOREM PROVING; VECTORS;

COHEN-GROSSBERG NEURAL NETWORKS; GLOBAL EXPONENTIAL CONVERGENCE; GLOBAL EXPONENTIAL STABILITY; M-MATRIX; TIME DELAY;

NEURAL NETWORKS;

ARTIFICIAL NEURAL NETWORK; LETTER; TIME;

NEURAL NETWORKS (COMPUTER); TIME FACTORS;

EID: 1242308776     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2003.822974     Document Type: Letter

References (15)

1. M. Araki, "Application of M-matrices to the stability problems of composite dynamical systems," J. Math. Anal. Appl., vol. 52, pp. 309-321, 1975.
2. J. Belair, "Stability in a model of a delayed neural networks," J. Dynam. Differential Equations, vol. 5, pp. 607-623, 1993.
3. Y. J. Cao and Q. H. Wu, "A note on stability of analog neural networks with time delays," IEEE Trans. Neural Networks, vol. 7, pp. 1533-1535, 1996.
4. J. Cao, "On exponentially stability and periodic solution of CNN's with delay," Phys. Lett. A, vol. 267, pp. 312-318, 2000.
5. T. P. Chen, "Convergence of delayed dynamical systems," Neural Processing Lett., vol. 10, no. 3, pp. 267-271, 1999.
6. T. P. Chen and S. Amari, "Stability of asymmetric hopfield networks," IEEE Trans. Neural Networks, vol. 12, pp. 159-163, 2001.
7. M. A. Cohen and S. Grossberg, "Absolute stability and global pattern formation and parallel memory storage by competitive neural networks," IEEE Trans. Syst., Man Cybern., vol. SMC-13, pp. 815-821, 1983.
8. K. H. Jack, "Sufficient conditions for stability and instability of autonomous functional-differential equations," J. Differential Equations, vol. 1, pp. 452-428, 1965.
9. R. H. Paul, Measure Theory: Van Nostrand, 1950.
10. H. Lu, "On stability of nonlinear continuous-time neural networks with delays," Neural Networks, vol. 13, no. 10, pp. 1135-1144, 2000.
11. K. M. Richard, "Asymptotic behavior of nonlinear delayed-differential equations," J. Differential Equations, vol. 1, pp. 293-305, 1995.
12. C. M. Marcus and R. M. Westervelt, "Stability of analog neural networks with delay," Phys. Rev. A., vol. 39, pp. 347-359, 1989.
13. L. Wang and X. Zou, "Exponential stability of cohen-grossberg neural networks," Neural Networks, vol. 15, pp. 415-422, 2002.
14. H. Ye, A. N. Michel, and K. Wang, "Qualitative analysis of cohen-grossberg neural networks with multiple delays," Phys. Rev. E, vol. 51, pp. 2611-2618, 1995.
15. J. Zhang and X. Jin, "Global stability analysis in delayed hopfield neural models," Neural Networks, vol. 13, no. 7, pp. 745-753, 2000.