Global exponential stability of competitive neural networks with different time scales

IEEE Transactions on Neural Networks

Volumn 14, Issue 3, 2003, Pages 716-719

  Meyer Baese, A ^a   Pilyugin, S S ^b   Chen, Y ^b  

^a FAMU FSU COLLEGE OF ENGINEERING   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Flow invariance; Global exponential stability; Multitime scale neural network

Indexed keywords

ASYMPTOTIC STABILITY; COGNITIVE SYSTEMS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; LEARNING ALGORITHMS; LYAPUNOV METHODS; MAXIMUM PRINCIPLE; PROBABILITY DISTRIBUTIONS;

COMPETITIVE NEURAL NETWORKS; FLOW INVARIANCE; GLOBAL EXPONENTIAL STABILITY; MULTITIME SCALE NEURAL NETWORK;

NEURAL NETWORKS;

EID: 0037507236     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2003.810594     Document Type: Letter

References (11)

1. S. Amari, "Field theory of self-organizing neural nets," IEEE Trans. Syst., Man, Cybern., vol. SMC-13, pp. 741-748, 1983.
2. ____, "Competitive and cooperative aspects in dynamics of neural excitation and self-organization," Competition Cooperation Neural Networks, vol. 20, pp. 1-28, 1982.
3. S. Grossberg, "Adaptive pattern classification and universal recording," Biol. Cybern., vol. 23, pp. 121-134, 1976.
4. ____, "Competition, decision and consensus," J. Math. Anal. Applicat., vol. 66, pp. 470-493, 1978.
5. D. Hebb, The Organization of Behavior. New York: J. Wiley, 1949.
6. M. Lemmon and V. Kumar, "Emulating the dynamics for a class of laterally inhibited neural networks," Neural Networks, vol. 2, pp. 193-214, 1989.
7. A. Meyer-Bäse, F. Ohl, and H. Scheich, "Singular perturbation analysis of competitive neural networks with different time-scales," Neural Comput., vol. 8, pp. 545-563, 1996.
8. L. Jin and M. Gupta, "Stable dynamic backpropagation learning in recurrent neural networks," IEEE Trans. Neural Networks, vol. 10, pp. 1321-1334, Nov. 1999.
9. M. Galicki, L. Leistritz, and H. Witte, "Learning continuous trajectories in recurrent neural networks with time-dependent weights," IEEE Trans. Neural Networks, vol. 10, pp. 741-756, May 1999.
10. J. Suykens, B. Moor, and J. Vandewalle, "Robust local stability of multilayer recurrent neural networks," IEEE Trans. Neural Networks, vol. 11, pp. 222-229, Jan. 2000.
11. D. Willshaw and C. von der Malsburg, "How patterned neural connections can be set up by self-organization," Proc. Roy. Soc. London B, vol. 194, pp. 431-445, 1976.