Qualitative analysis of competitive-cooperative cellular neural networks with delay

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 15, Issue 1, 2002, Pages 457-462

  Chu, Tianguang ^a   Zhang, Cishen ^b   Wang, Zhaolin ^c  

^a PEKING UNIVERSITY   (China)

^b UNIVERSITY OF MELBOURNE   (Australia)

^c TSINGHUA UNIVERSITY   (China)

Author keywords

Cellular neural networks; Competition and cooperation; Convergence; Monotone dynamical system; Stability; Time delay; Trapping region

Indexed keywords

AUTOMATION; CONVERGENCE OF NUMERICAL METHODS; DECAY (ORGANIC); DYNAMICAL SYSTEMS; TIME DELAY;

CELLULAR NEURAL NETWORKS WITH DELAYS; COMPETITION AND COOPERATION; CONNECTION WEIGHTS; CONVERGENCE; DELAYED CELLULAR NEURAL NETWORKS; MONOTONE DYNAMICAL SYSTEMS; QUALITATIVE ANALYSIS; TRAPPING REGIONS;

CELLULAR NEURAL NETWORKS;

EID: 84945551071     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20020721-6-es-1901.00729     Document Type: Conference Paper

References (23)

1. Arik, S. and V. Tavsanoglu (2000). On the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Circuit Syst. I, 47, 571-574.
2. Berman, A. and R.J. Plemmons (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York.
3. Cao, J. (1999). Periodic solutions and exponential stability in delayed cellular neural networks. Phys. Rev. E, 60, 3244-3248.
4. Cao, J. (2000). On exponential stability and periodic solutions of CNNs with delays. Phys. Lett. A, 267, 312-318.
5. Chu, T. (2001). Convergence in discrete-time neural networks with specific performance. Phys. Rev. E, 63, 0519041-0519045.
6. Chu, T. and L. Huang (1998). Mixed monotone decomposition of dynamical systems with application. Chinese Science Bulletin, 43, 1171-1175.
7. Chu, T., L. Huang and L. Wang (2001a). Guaranteed absolute stability and robustness of a class of delay systems with local sector nonlinearities via piecewise linear Lyapunov function. Proc. ACC, Arlington, VA, 4212-4217.
8. Chu, T. and Z. Wang (1998). Competitive and cooperative dynamics in neural networks with transmission delays (in Chinese). In: Studies in Dynamics, Vibration and Control (B. Chen (Ed)), 150-154, Hunan University Press, Changsha.
9. Chu, T., Z. Wang and L. Wang (2001b). Exponential convergence estimate for analog neural networks with multiple delays. Proc. 40th IEEE CDC, Orlando, FL, 2715-2719.
10. Chua, L.O. and L. Yang (1988). Cellular neural networks: Theory and applications. IEEE Trans. Circuits Syst., 35, 1257-1290.
11. Chua, L.O. and C.W. Wu (1992). On the universe of stable cellular neural networks. Int. J. Circuit Theory AppL, 20, 497-517.
12. Civalleri, P.P., M. Gill and L. Pandolfi (1993). On stability of cellular neural networks with delay. IEEE Trans. Circuit Syst., 40, 157-164.
13. Gill, M. (1994). Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Trans. Circuit Syst. I, 41, 518-528.
14. Hirsch, M.W. (1989). Convergent activation dynamics in continuous time networks. Neural Networks, 2, 331-349.
15. Lemmon, M. and B.V.K. Vijaya Kumar (1989). Emulating the dynamics for a class of laterally inhibited neural networks. Neural Networks, 2, 193-214.
16. Michel, A.N., J.A. Farrell and W. Porod (1989). Qualitative analysis of neural networks. IEEE Trans. Circuits Syst., 36, 229-243.
17. Ohta, Y. (1981). Qualitative analysis of nonlinear quasi-monotone dynamical systems described by functional-differential equations. IEEE Trans. Circuits Syst., 28, 138-144.
18. Roska, T. and L.O. Chua (1992). Cellular neural networks with nonlinear and delay-type template elements and nonuniform grids. Int. J. Circuit Theory AppL, 20, 469-481.
19. Roska, T., C.W. Wu, M. Balsi and L.O. Chua (1992). Stability and dynamics of delay-type general cellular neural networks. IEEE Trans. Circuit Syst. I, 39, 487-490.
20. Roska, T., C.W. Wu and L.O. Chua (1993). Stability of cellular neural networks with dominant nonlinear and delay-type templates. IEEE Trans. Circuit Syst. I, 40, 270-272.
21. Takahashi, N. (2000). A new sufficient condition for complete stability of cellular neural networks with delay. IEEE Trans. Circuit Syst. I, 47, 793-799.
22. van den Driessche, P. and X. Zou (1998). Global attractivity in delayed Hopfield neural network models. SIAM J. Appl. Math., 58, 1878-1890.
23. van den Driessche, P., J. Wu and X. Zou (2001). Stabilization role of inhibitory self-connections in a delayed neural network. Physica D, 150, 84-90.