Multistability of two kinds of recurrent neural networks with activation functions symmetrical about the origin on the phase plane

IEEE Transactions on Neural Networks and Learning Systems

Volumn 24, Issue 11, 2013, Pages 1749-1762

  Zeng, Zhigang ^a,b,c   Zheng, Wei Xing ^a  

^a UNIVERSITY OF WESTERN SYDNEY   (Australia)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

Attractive set; equilibrium point; multistability; time varying delays

Indexed keywords

ACTIVATION FUNCTIONS; ATTRACTIVE SET; EQUILIBRIUM POINT; EXPONENTIALLY STABLE; MULTI STABILITIES; PHASE PLANE; TIME-VARYING DELAY;

TIME VARYING CONTROL SYSTEMS;

RECURRENT NEURAL NETWORKS;

ALGORITHM; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; COMPARATIVE STUDY; COMPUTER SIMULATION; FEEDBACK SYSTEM; PROCEDURES; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED;

EID: 84886853973     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2262638     Document Type: Article

References (30)

1. S. Grossberg, "Nonlinear difference-differential equations in prediction and learning theory," Proc. Nat. Acad. Sci., vol. 58, no. 4, pp. 1329-1334, 1967
2. S. Grossberg, "Global ratio limit theorems for some nonlinear functional differential equations I," Bull. Amer. Math. Soc., vol. 74, no. 1, pp. 95-99, 1968
3. L. O. Chua and L. Yang, "Cellular neural networks: Theory," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1257-1272, Oct. 1988
4. L. O. Chua and L. Yang, "Cellular neural networks: Applications," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1273-1290, Oct. 1988
5. T. Roska, C. W. Wu, M. Balsi, and L. O. Chua, "Stability and dynamics of delay-type general and cellular neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 39, no. 6, pp. 487-490, Jun. 1992
6. T. Roska, C. W. Wu, and L. O. Chua, "Stability of cellular neural networks with dominant nonlinear and delay-type templates," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 4, pp. 270-272, Apr. 1993
7. D. Liu, S. Hu, and J. Wang, "Global output convergence of a class of continuous-time recurrent neural networks with time-varying thresholds," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 51, no. 4, pp. 161-167, Apr. 2004
8. S. Hu and D. Liu, "On the global output convergence of a class of recurrent neural networks with time-varying inputs," Neural Netw., vol. 18, no. 2, pp. 171-178, 2005 (Pubitemid 40431615)
9. H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability of recurrent neural networks with multiple time varying delays," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 855-873, May 2008 (Pubitemid 351728821)
10. H. Zhang, Z. Wang, and D. Liu, "Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time varying delays," IEEE Trans. Neural Netw., vol. 19, no. 11, pp. 1942-1955, Nov. 2008
11. H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability and robust stability of a general class of Cohen-Grossberg neural networks with mixed delays," IIEEE Trans. Circuits Syst. I, Reg. Papers, vol. 56, no. 3, pp. 616-629, Mar. 2009
12. Z. G. Zeng, J. Wang, and X. X. Liao, "Stability analysis of delayed cellular neural networks described using cloning templates," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 11, pp. 2313-2324, Nov. 2004
13. Z. G. Zeng and J. Wang, "Design and analysis of high-capacity associative memories based on a class of discrete-time recurrent neural networks," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 6, pp. 1525-1536, Dec. 2008
14. Z. Yi, K. K. Tan, and T. H. Lee, "Multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions," Neural Comput., vol. 15, no. 3, pp. 639-662, Mar. 2003 (Pubitemid 37049820)
15. C. Y. Cheng, K. H. Lin, and C. W. Shih, "Multistability in recurrent neural networks," SIAM J. Appl. Math., vol. 66, no. 4, pp. 1301-1320, Jul. 2006
16. J. D. Cao, G. Feng, and Y. Y. Wang, "Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions," Phys. D, Nonlinear Phenomena, vol. 237, no. 13, pp. 1734-1749, Aug. 2008
17. L. Zhang, Z. Yi, and J. Yu, "Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions," IEEE Trans. Neural Netw., vol. 19, no. 1, pp. 158-167, Jan. 2008 (Pubitemid 351279234)
18. L. Zhang, Z. Yi, S. L. Zhang, and P. A. Heng, "Activity invariant sets and exponentially stable attractors of linear threshold discrete-time recurrent neural networks," IEEE Trans. Autom. Control, vol. 54, no. 6, pp. 1341-1347, Jun. 2008
19. L. Zou, H. J. Tang, K. C. Tan, and W. N. Zhang, "Nontrivial global attractors in 2-D multistable attractor neural networks," IEEE Trans. Neural Netw., vol. 20, no. 11, pp. 1842-1851, Nov. 2009
20. L. L. Wang, W. L. Lu, and T. P. Chen, "Multistability and new attraction basins of almost-periodic solutions of delayed neural networks," IEEE Trans. Neural Netw., vol. 20, no. 10, pp. 1581-1593, Oct. 2009
21. Z. G. Zeng, T. W. Huang, and W. X. Zheng, "Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function," IEEE Trans. Neural Netw., vol. 21, no. 8, pp. 1371-1377, Aug. 2010
22. L. L. Wang, W. L. Lu, and T. P. Chen, "Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions," Neural Netw., vol. 23, no. 2, pp. 189-200, 2010
23. Z. G. Zeng and W. X. Zheng, "Multistability of neural networks with time-varying delays and concave-convex characteristics," IEEE Trans. Neural Netw. Learning Syst., vol. 23, no. 2, pp. 293-305, Feb. 2012
24. K. Yosida, Functional Analysis Berlin, Germany: Springer-Verlag, 1978
25. Z. G. Zeng and J. Wang, "Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks," Neural Comput., vol. 18, no. 4, pp. 848-870, 2006 (Pubitemid 43543824)
26. H. Li, J. Lam, and K. C. Cheung, "Passivity criteria for continuous-time neural networks with mixed time-varying delays," Appl. Math. Comput., vol. 218, no. 22, pp. 11062-11074, Jul. 2012
27. Q. Song and J. Cao, "Passivity of uncertain neural networks with both leakage delay and time-varying delay," Nonlinear Dyn., vol. 67, no. 2, pp. 1695-1707, 2012
28. S. Li, S. Chen, and B. Liu, "Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function," Neural Process. Lett., vol. 37, no. 2, pp. 189-205, Apr. 2013
29. S. Li, Y. Li, and Z. Wang, "A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application," Neural Netw., vol. 39, pp. 27-39, Mar. 2013
30. S. Li, B. Liu, and Y. Li, "Selective positive-negative feedback produces the ?winner-take-all competition in recurrent neural networks," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 2, pp. 301-309, Feb. 2013.