On complex artificial higher order neural networks: Dealing with stochasticity, jumps and delays

Artificial Higher Order Neural Networks for Economics and Business

Volumn , Issue , 2008, Pages 466-483

  Wang, Zidong ^a   Liu, Yurong ^b   Liu, Xiaohui ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

^b YANGZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052597142     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4018/978-1-59904-897-0.ch021     Document Type: Chapter

References (35)

1. Arik, S. (2005). Global robust stability analysis of neural networks with discrete time delays. Chaos, Solitons and Fractals, 26(5), 1407-1414.
2. Artyomov, E., & Yadid-Pecht, O. (2005). Modified high-order neural network for invariant pattern recognition. Pattern Recognition Letters, 26(6), 843-851.
3. Bengio, Y., Frasconi, P., & Simard, P. (1993). The problem of learning long-term dependencies in recurrent networks. In Proc. 1993 IEEE Int. Conf. Neural Networks, vol. 3, pp.1183-1188.
4. Blythe, S., Mao, X. & Liao, X. (2001). Stability of stochastic delay neural networks. Journal of the Franklin Institute, 338, 481-495.
5. Boyd, S., Ei Ghaoui, L., Feron, E. & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia, PA: SIAM.
6. Cao, J., & Chen, T. (2004). Globally exponentially robust stability and periodicity of delayed neural networks. Chaos, Solitons and Fractals, 22(4), 957-963.
7. Cao, J., Huang, D.-S. & Qu, Y. (2005). Global robust stability of delayed recurrent neural networks. Chaos, Solitons and Fractals, 23, 221-229.
8. Cao, J., Liang, J., & Lam, J. (2004). Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D: Nonlinear Phenomena, 199(3-4), 425-436.
9. Casey, M.P. (1996). The dynamics of discrete-time computation with application to recurrent neural networks and finite state machine extraction. Neural Comput., 8(6), 1135-1178.
10. Dembo, A., Farotimi, O., & Kailath, T. (1991). High-order absolutely stable neural networks. IEEE Trans. Circuits Syst., 38(1), 57-65.
11. Gahinet, P., Nemirovsky, A., Laub A.J., & Chilali, M. (1995). LMI control toolbox: For use with Matlab. The Math Works, Inc.
12. Giles, C.L., & Maxwell T. (1987). Learning, invariance, and generalization in high-order neural networks. Appl. Optics, 26(23), 4972-4978.
13. Gu, K. (2000). An integral inequality in the stability problem of time-delay systems. In Proceedings of 39th IEEE Conference on Decision and Control, December 2000, Sydney, Australia, pp. 2805-2810.
14. Hale, J.K. (1977). Theory of functional differential equations. New York: Springer-Verlag.
15. Huang, H., Ho, D. W. C, & Lam, J. (2005). Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans. Circuits and Systems: Part II, 52(5), 251-255.
16. Huang, H., Qu, Y., & Li, H.X. (2005). Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Physics Letters A, 345(4-6), 345-354.
17. Ji, Y., & Chizeck, H.J. (1990). Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control, 35, 777-788.
18. Kappen, H. J. (2001). An introduction to stochastic neural networks. In Stan Gielen and Frank Moss (Eds.), Handbook of biological physics, pp.517-552. Elsevier.
19. Karayiannis, N. B., & Venetsanopoulos, A. N. (1995). On the training and performance of highorder neural networks. Mathematical Biosciences, 129(2), 143-168.
20. Khasminskii, R. Z. (1980). Stochastic stability of differential equations. Alphen aan den Rijn, Sijthoffand Noor, Khasminskiidhoff.
21. Lai, T.L., & Wong, P.S. (2001). Stochastic neural networks with applications to nonlinear time series. Journal of the American Statistical Association, 96(455), 968-981.
22. Lu, Z., Shieh, L.-S., Chen G., & Coleman, N. P. (2006). Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks. Information Sciences, 176(16), 2337-2354.
23. Psaltis D., Park, C. H., & Hong, J. (1988). Higher order associative memories and their optical implementations. Neural Networks, 1, 143-163.
24. Ren, F., & Cao, J. (2006). LMI-based criteria for stability of high-order neural networks with timevarying delay. Nonlinear Analysis Series B: Real World Applications, 7(5), 967-979.
25. Skorohod, A. V. (1989). Asymptotic methods in the theory of stochastic differential equations. Providence, RI: Amer. Math. Soc.
26. Tino, P., Cernansky, M. & Benuskova, L. (2004). Markovian architectural bias of recurrent neural networks. IEEE Trans. Neural Networks, 15(1), 6-15.
27. Wan, L., & Sun, J. (2005). Mean square exponential stability of stochastic delayed Hopfield neural networks. Physics Letters A, 343(4), 306-318.
28. Wang, Z., Fang, J. & Liu, X. (2008). Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos, Soliton & Fractals, 36(2), pp. 388-396.
29. Wang, Z., Liu, Y., Li, M., & Liu, X. (2006a). Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Networks, 17(3), 814-820.
30. Wang, Z., Liu, Y., Fraser, K., & Liu, X. (2006b). Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Physics Letters A, 354(4), 288-297.
31. Wang, Z., Liu, Y., Yu, L., & Liu, X. (2006c). Exponential stability of delayed recurrent neural networks with Markovian jumping parameters, Physics Letters A, 356(4-5), 346-352.
32. Xu, B., Liu, X., & Liao, X. (2005). Global asymptotic stability of high-order Hopfield type neural networks with time delays. Computers & Mathematics with Applications, 45(10-11), 1729-1737.
33. Zhang, J., Shi, P., & Qiu, J. (2007). Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays. Nonlinear Analysis: Real World Applications, 8(4), 1349-1357
34. Zhao, H. (2004a). Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Networks, 17, 47-53.
35. Zhao, H. (2004b). Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Applied Mathematics and Computation, 154, 683-695.