Global robust stability of competitive neural networks with continuously distributed delays and different time scales

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4668 LNCS, Issue PART 1, 2007, Pages 569-578

  Kao, Yonggui ^a   Ming, QingHe ^a  

^a ZAOZHUANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BRAIN; DIFFERENCE EQUATIONS; LEARNING ALGORITHMS; NEURONS; STABILITY CRITERIA; TOPOLOGY;

COMPETITIVE NEURAL NETWORK; CONTINUOUSLY DISTRIBUTED DELAYS; DIFFERENT TIME SCALE; EXISTENCE AND UNIQUENESS; GLOBAL ROBUST STABILITY; LIAPUNOV FUNCTIONAL METHOD; LONG AND SHORT TERM MEMORY; SYNAPTIC MODIFICATION;

NEURAL NETWORKS;

EID: 38149015594     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-74690-4_58     Document Type: Conference Paper

References (32)

1. Meyer-Base, A., Ohl, F., Scheich, H.: Singular perturbation analysis of competitive neural networks with different time-scales. Neural Computation 8, 1731-1742 (1996)
2. Meyer-Baese, A., Pilyugin, S.S., Chen, Y.: Global Exponential Stability of Competitive Neural Networks With Different Time Scale. IEEE Tran. Neural Networks 14, 716-719 (2003)
3. Meyer-Baese, A., et al.: Local exponential stability of competitive neural networks with different time scales. Engineering Applications of Artificial Intelligence 17, 227-232 (2004)
4. Lu, H., He, Z.: Global exponential stability of delayed competitive neural networks with different time scales. Neural Networks 18, 243-250 (2005)
5. Grossberg, S.: Competition,Decision and Consensus. J.Math.Anal.Applicat 66, 470-493 (1978)
6. Amari, S.: Competitive and Cooperater Aspects in Dynamics of Neural Excition and Self-organization. Competition Cooperation Neural Networks 20, 1-28 (1982)
7. Cohen, A.M., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics 13, 815-826 (1983)
8. Lemmon, M., Kumar, M.: Emulating the dynamics for a class of laterally inhibited neural networks. Neural Networks 2, 193-214 (1989)
9. Zhang, Q., Wei, X.P., Xu, J.: Global exponential stability of Hopfield neural networks with continuously distributed delays. Phys.Lett. A 315(6), 431-436 (2003)
10. Zhang, Q., MA, R.N., XU, J.: Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays. Communications in Theoretical Physics 39(3), 381-384 (2003)
11. Zhang, Q., MA, R.N., XU, J.: Global stability of bidirectional associative memory neural networks with continuously distributed delays. Science in China, Ser.F 46(5), 327-334 (2003)
12. Cao, J., Huang, D.S., Qu, Y.: Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals 23(1), 221-229 (2005)
13. Ye, H., Michel, A.N.: Robust stability of nonlinear time-delay systems with applications to neural networks. IEEE Trans. Circuits Syst. I 43, 532-543 (1996)
14. Hu, S.Q., Wang, J.: Global exponential stability of continuous-time interval neural networks. Phys. Rev. E 65, 36-133 (2002)
15. Liao, X.F., Yu, J.B.: Robust stability for interval Hopfield neural networks with time delay. IEEE Trans. Neural Netw. 9, 1042-1045 (1998)
16. Liao, X.F., Wong, K.W., Wu, Z., Chen, G.: Novel robust stability for intervaldelayed hopfield neural networks. IEEE Trans. Circuits Syst. I 48, 1355-1359 (2001)
17. Arik, S.: Global robust stability of delayed neural networks. IEEE Trans. Circuits Syst. I 50(1), 156-160 (2003)
18. Cao, J., Chen, T.: Globally exponentially robust stability and periodicity of delayed neural networks. Chaos Solitons Fractals 22(4), 957-963 (2004)
19. Wang, L., Gao, Y.: Global exponential robust stability of reaction-diffuion internal neural networks with time-varing delays. Physics letters A 350, 342-348 (2006)
20. Wang, L.S., Gao, Y.Y: On global robust stability for interval Hopfield neural networks with time delays. Ann. Differential Equations 19(3), 421-426 (2003)
21. Liao, X.X.: Theory,Methods and Analysis of Stability, Huazhong University of Science and Technology Publishing House, Wuhan (1996)
22. Guo, D.J., Sun, J.X., liu, Z.L.: Functional Methods of Nonlinear Ordinary Differential Equations. Shangdong Science Press, Jinan (1995)
23. Gopalsamy, K.: Stability and Oscillation in Delay Differential Equation of Population Dynamics, Dordrecht Netherlands. Kluwer Academic Publishers, Boston, MA (1992)
24. Kao, Y., Gao, C.: Global Stability of Bidirectional Associative Memory Neural Networks with Variable Coecients and S-Type Distributed Delays. In: King, I., Wang, J., Chan, L., Wang, D. (eds.) ICONIP 2006. LNCS, vol. 4232, pp. 598-607. Springer, Heidelberg (2006)
25. Kao, Y., Gao, C. (eds.): Global Asymptotic Stability of Cellular Neutral Networks With Variable Coefficients and Time-Varying Delays. LNCS, vol. 4491, pp. 923-924. Springer, Heidelberg (2007)
26. Zhang, Q., Wei, X., Xu, J.: Asymptotic stability of transiently chaotic neural networks. Nonlinear Dynamics 42(4), 339-346 (2005)
27. Zhang, Q., Wei, X., Xu, J.: A new global stability result for delayed neural networks. Nonlinear Analysis: Real World Applications 8(3), 1024-1028 (2007)
28. Zhang, Q., Wei, X., Xu, J.: Global exponential stability for nonautonomous cellular neural networks with delays. Phys.Lett. A 351, 153-160 (2005)
29. Zhang, Q., Wei, X., Xu, J.: An improved result for complete stability of delayed cellular neural networks. Automatica 41(2), 333-337 (2005)
30. Zhang, Q., Ma, R., Xu, J.: Delay-independent stability in cellular neural networks with infinite delays. Chinese Journal of Electronics 12(2), 189-192 (2003)
31. Zhang, Q., Wei, X., Xu, J.: Global asymptotic stability of cellular neural networks with infinite delay. Neural Network World 15(6), 579-589 (2005)
32. Zhang, Q., Zhou, C.: Dynamics of Hopfield neural networks with continuously distributed delays. Dynamics of Continuous, Discrete and Impulsive Systems-Series A-Mathematical Analysis, Part 2 Suppl. S 13, 541-544 (2006)