Complex dynamics in simple Hopfield neural networks

Chaos

Volumn 16, Issue 3, 2006, Pages

  Yang, Xiao Song ^a   Huang, Yan ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749322790     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2220476     Document Type: Article

References (24)

1. J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Natl. Acad. Sci. U.S.A. 81, 3088 (1984).
2. H. Bersini and P. Sener, "The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks," Neural Networks 15, 1197 (2002).
3. M. R. Guevara, L. Glass, M. C. Mackay, and A. Shrier, "Chaos in neurobiology," IEEE Trans. Syst. Man Cybern. 13, 790 (1983).
4. A. Babloyantz and C. Lourenco, "Brain chaos and computation," Int. J. Neural Syst. 7, 461 (1996).
5. G. Dror and M. Tsodyks, "Chaos in neural networks with dynamic synapses," Neurocomputing 32-33, 365 (2000).
6. P. Arena, S. Baglio, L. Fortuna, and G. Manganaro, "Hyperchaos from cellular neural networks," Electron. Lett. 31, 250 (1995).
7. A. Das, P. Das, and A. B. Roy, "Chaos in a three-dimensional general model of neural network," Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 2271 (2000).
8. H. Bersini, "The frustrated and compositional nature of chaos in small Hopfield networks," Neural Networks 11, 1017 (1998).
9. Q. Li, X.-S. Yang, and F. Yang, "Hyperchaos in Hopfield-type neural networks," Neurocomputing 67, 275 (2005).
10. X.-S. Yang and Q. Yuan, "Chaos and transient chaos in simple Hopfield neural networks," Neurocomputing 69, 232 (2005).
11. X.-S. Yang and Q. Li, "Horseshoe chaos in cellular neural networks," Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, 157 (2006).
12. J. E. Lewis and L. Glass, "Steady states, limit cycles, and chaos in models of complex biological networks," Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 477 (1991).
13. J. E. Lewis and L. Glass, "Nonlinear dynamics and symbolic dynamics of neural networks," Neural Comput. 4, 621 (1992).
14. R. Edwards, "Analysis of continuous-time switching networks," Physica D 146, 165 (2000).
15. R. Edwards and L. Glass, "Combinatorial explosion in model gene networks," Chaos 10, 691 (2000).
16. T. Mestl, C. Lemay, and L. Glass, "Chaos in high-dimensional neural and gene networks," Physica D 98, 35 (1996).
17. T. Mestl, E. Plahte, and S. W. Omholt, "Periodic solutions in systems of piecewise-linear differential equations," Dyn. Stab. Syst. 10, 179 (1995).
18. X.-S. Yang and Y. Tang, "Horseshoes in piecewise continuous maps," Chaos, Solitons Fractals 19, 841 (2004).
19. X.-S. Yang, "Metric horseshoes," Chaos, Solitons Fractals 20, 1149 (2004).
20. X.-S. Yang, H.-M. Li, and Y. Huang, "A planar topological horseshoe theory with applications to computer verifications of chaos," J. Phys. A 38, 4175 (2005).
21. K. Ramasubramanian and M. S. Sriram, "A comparative study of computation of Lyapunov spectra with different algorithms," Physica D 139, 72 (2000).
22. J. P. Eckmann and D. Ruelle, "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 617 (1985).
23. S. Wiggins, Introduction to Applied Nonlinear dynamical Systems and Chaos (Springer-Verlag, New York, 1990).
24. C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos (CRC Press, Florida, 1995).