Strange attractors in chaotic neural networks

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 47, Issue 10, 2000, Pages 1455-1468

  Chen, Luonan ^a   Aihara, Kazuyuki ^a  

^a OSAKA SANGYO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); CHAOS THEORY; ELECTRIC NETWORK ANALYSIS; ELECTRIC NETWORK SYNTHESIS; ELECTRIC NETWORK TOPOLOGY; FEEDBACK CONTROL; OPTIMIZATION; TRANSIENTS;

ATTRACTORS; HOMOCLINIC BIFURCATION; SNAP BACK REPELLERS; TRANSIENT CHAOTIC NEURAL NETWORKS (TCNN);

NEURAL NETWORKS;

EID: 0034292043     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.886976     Document Type: Article

References (29)

1. M. Adachi and K. Aihara, "Associative dynamics in a chaotic neural network," Neural Networks, vol. 10, no. 1, pp. 83-98, 1997.
2. "An analysis of instantaneous stability of an associative chaotic neural network," Int. J. Bifurcation and Chaos, vol. 9, no. 11, pp. 2157-2163, 1999.
3. S. Amari, "Characteristics of random nets of analog neuron-like elements," IEEE Trans. Syst., Man, Cybern., vol. SMC-2, pp. 643-657, 1972.
4. K. Aihara, T. Takabe, and M. Toyoda, "Chaotic neural networks," Phys. Lett. A, vol. 144, no. 6/7, pp. 333-340, 1990.
5. J. Buescu, Exotic Attractors from Liapunov Stability to Riddled Basins. Basel: Birkhaüser Verlag, 1997.
6. L. Chen and K. Aihara, "Transient chaotic neural networks and chaotic simulated annealing," Toward the Harnessing of Chaos, M. Yamaguti, Ed. Amsterdam, The Netherlands: Elsevier, 1994, pp. 347-352.
7. "Chaotic simulated annealing for combinatorial optimization," in Dynamic Systems and Chaos, Aoki et al., Eds. Singapore: World Scientific, 1995, vol. 1, pp. 319-322.
8. "Chaotic simulated annealing by a neural network model with transient chaos," Neural Networks, vol. 8, no. 6, pp. 915-930, 1995.
9. "Chaos and asymptotical stability in discrete-time neural networks," Physica D, vol. 104, pp. 286-325, 1997.
10. L. Chen, H. Suzuki, and K. Katou, "Mean field theory for optimal power flow," IEEE Trans. Power Syst., vol. 12, no. 4, pp. 1481-1486, 1997.
11. L. Chen and K. Aihara, "Global searching ability of chaotic neural networks," IEEE Trans. Circuits Syst. l, vol. 46, no. 8, pp. 974-993, 1999.
12. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed. Reading, MA: Addison-Wesley, 1989.
13. J. P. Eckmann and Ruelle, "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys., vol. 57, no. 3, pp. 617-656, 1985.
14. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1983.
15. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic, 1974.
16. J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities: Proc. Nat. Acad. Sci., 1982, vol. 79, pp. 2554-2558.
17. Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state Neurons: Proc. Nat. Acad. Sci., 1984, vol. 81, pp. 3088-3092.
18. J. Hopfield and D. Tank, "Neural computation of decisions in optimization problems," Biol. Cybern., vol. 52, pp. 141-152, 1985.
19. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory. New York: Springer-Verlag, 1995.
20. T. Y. Li and J. A. Yorke, "Period three implies chaos," Amer. Math. Monthly, vol. 82, pp. 985-992, 1975.
21. C. M. Marcus and R. M. Westervelt, "Dynamics of iterated-map neural networks," Phys. Rev. A, Gen. Phys., vol. 40, pp. 501-504, 1989.
22. n," J. Math. Anal. Appl., vol. 63, pp. 199-223, 1978.
23. C. Mira, L. Gardini, A. Barugola, and J. Cathala, Chaotic Dynamics in Two-Dimensional Noninvertible Maps. Singapore: World Scientific, 1995.
24. C. Peterson and J. R. Anderson, "A mean field theory algorithm for neural networks," Complex Systems, vol. 1, pp. 995-1019, 1989.
25. C. Peterson and B. Soderberg, "Artificial neural networks," Modern Heuristic Techniques for Combinatorial Problems, C. R. Reeves, Ed. London, U.K.: Blackwell Scientific, 1993.
26. E. A. Razafimanantena, "Analysis of the dynamics of Aihara's model of chaotic neural networks,", preprint, 1997.
27. D. E. Rumelhart, J. L. McClelland, and PDP Research Group, Parallel Distributed Processing: MIT Press, 1986, vol. 1 & 2.
28. I. Shimada and T. Nagashima, "A numerical approach to ergodic problem of dissipative dyanmical systems," Prog. Theor. Phys., vol. 61, pp. 1605-1616, 1979.
29. M. Urabe, "Galerkin's procedure for nonlinear periodic systems," ARCH. Rat. Mech. Anal., vol. 72, pp. 121-152, 1965.