Horseshoe and topological entropy estimate of a class of three-dimensional cellular neural networks

Applied Mathematics and Computation

Volumn 197, Issue 1, 2008, Pages 382-388

  Liao, Zhensong ^a   Huang, Yan ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Cellular neural networks; Chaos; Poincar map; Topological entropy; Topological horseshoe

Indexed keywords

CHAOS THEORY; CONFORMAL MAPPING; DYNAMICAL SYSTEMS; NUMERICAL METHODS; PARAMETER ESTIMATION; THREE DIMENSIONAL;

CHAOTIC BEHAVIOR; POINCARE MAPS; TOPOLOGICAL ENTROPY; TOPOLOGICAL HORSESHOE;

CELLULAR NEURAL NETWORKS;

EID: 38949205215     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.07.077     Document Type: Article

References (18)

1. Chua L.O., and Yang L. Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35 (1988) 1257-1272
2. Chua L.O., and Roska T. The CNN paradigm. IEEE Trans. Circuit Syst. I 40 (1993) 147-155
3. Chua L.O., and Roska T. Cellular Networks and Visual Computing (2002), Cambridge University Press
4. Arena P., Baglio S., et al. Hyperchaos from cellular neural networks. Electron. Lett. 31 (1995) 250-251
5. Y. Huang, X.S.Yang, Chaos and two-tori in a new family of 4-CNNs, Int. J. Bifurcation Chaos, in press.
6. Y. Huang, X.S.Yang, Hyperchaos in a new family of simple CNN, Int. J. Bifurcation Chaos, in press.
7. Y. Huang, X.S.Yang, Chaos and hyperchaos in a class of simple cellular neural networks modeled by ODE, Int. J. Bifurcation Chaos, in press.
8. Yang X.S., and Huang Y. A new class of chaotic simple 3-cell cellular neural network. Int. J. Bifurcation Chaos 16 (2006) 1019-1021
9. Zou F., and Nossek J.A. Bifurcation and chaos in cellular neural networks. IEEE Trans. Circuits Syst. I 40 (1993) 166-173
10. Yang X.S., and Tang Y. Horseshoes in piecewise continuous maps. Chaos Solitons Fractals 19 (2004) 841-845
11. Yang X.S. Metric horseshoes. Chaos Solitons Fractals 20 (2004) 1149-1156
12. 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
13. Yang X.S., and Li Q.D. Horseshoe chaos in cellular neural networks. Int. J. Bifurcation Chaos 16 (2006) 157-161
14. Yang X.S., and Li Q.D. Existence of horseshoes in a foodweb model. Int. J. Bifurcation Chaos 14 (2004) 1847-1852
15. Yang X.S., Tang Y., and Li Q.D. Horseshoe in two-scroll control systems. Chaos Solitons Fractals 21 (2004) 1087-1091
16. Ramasubramanian K., and Sriram M.S. A comparative study of computation of Lyapunov spectra with different algorithms. Physica D 139 (2000) 72-86
17. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos (1990), Springer, New York
18. Robinson C. Dynamical Systems: Stability Symbolic Dynamics and Chaos (1995), CRC Press Inc.