Horseshoe chaos in a class of simple Hopfield neural networks

Chaos, Solitons and Fractals

Volumn 39, Issue 4, 2009, Pages 1522-1529

  Yuan, Quan ^a   Li, Qingdu ^a   Yang, Xiao Song ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; TOPOLOGY;

CHAOTIC BEHAVIORS; HORSESHOE CHAOS; POINCARE; TOPOLOGICAL ENTROPY; TOPOLOGICAL HORSESHOES;

HOPFIELD NEURAL NETWORKS;

EID: 63449131397     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.06.037     Document Type: Article

References (21)

1. Hopfield J.J. Proc Natl Acad Sci USA 81 (1984) 3088
2. Freeman W.J., and Barrie J.M. Chaotic oscillations and the genesis of meaning in cerebral cortex. In: Buzsaki G., Linas R., Singer W., Berthoz A., and Christen Y. (Eds). Temporal coding in the brain (1994), Springer, Berlin 13-24
3. Guevara M.R., Glass L., Mackey M.C., and Shrier A. Chaos in neurobiology. IEEE Trans Syst Man Cybernetic 13 (1983) 790-798
4. Babloyantz A., and Lourenco C. Brain chaos and computation. Int J Neural Syst 7 (1996) 461-471
5. Korn H., and Faure P. Is there chaos in the brain? II. Experimental evidence and related models. CR Biologes 326 (2003) 785-855
6. Kaneko K., and Tsuda I. Complex systems: chaos and beyond: a constructive approach with applications in life sciences (2001), Springer
7. Das A., Das P., and Roy A.B. Chaos in a three-dimensional general model of neural network. Int J Bifurcat Chaos 12 10 (2000) 2271-2281
8. Yang X.S., and Li Q.D. Horseshoe chaos in cellular neural networks. Int J Bifurcat Chaos 16 (2006) 157-161
9. Yang X.S., and Yuan Q. Chaos and transient chaos in simple Hopfield neural networks. Neurocomputing 69 (2005) 232-239
10. Yang X.S. Metric horseshoe. Chaos Solitons & Fractals 20 5 (2004) 149-156
11. Yang X.S., Tang Y., and Li Q.D. Horseshoe in two-scroll control systems. Chaos, Solitons & Fractals 21 5 (2004) 1087-1091
12. Yang X.S., and Tang Y. Horseshoes in piecewise continuous maps. Chaos Solitons & Fractals 19 (2004) 841-844
13. Chen Y.C. Small horseshoe via the anti-integrability. Chaos, Solitons & Fractals 28 2 (2006) 377-378
14. Dai D., Ma Y., Tse C.K., and Ma X.K. Existence of horseshoe maps in current-mode controlled buck-boost dc/dc converters. Chaos, Solitons & Fractals 25 3 (2005) 549-556
15. Fan QJ, Yang XS. A computer-assisted proof of chaos in a Hopfield neural network. Chaos, Solitons & Fractals; in press.
16. Wiggins. Introduction to applied nonlinear dynamical systems and chaos (1990), Springer-Verlag, New York
17. Yang X.S., Li H.M., and Huang Y. A planar topological horseshoe theory with applications to computer verifications of chaos. J Phys A: Math Gen 38 (2005) 4175-4185
18. Robinson C. Dynamical systems: stability, symbolic dynamics, and chaos (1995), CRC Press, Boca Raton, FL
19. Yang X.S., and Li Q.D. Existence of horseshoes in a foodweb model. Int J Bifurcat Chaos 14 5 (2004) 1847-1852
20. Eckmann J.P., and Ruelle D. Ergodic theory of chaos and strange attractors. Rev Mod Phys 57 3 (1985) 617-639
21. Franks J., and Williams R.F. Entropy and knots. Trans Am Math Soc 291 (1985) 241-248