Nonlinear computability based on chaos

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 2, 2000, Pages 415-429

  Manganaro, Gabriele ^a   De Gyvez, Jose Pineda ^b  

^a TEXAS INSTRUMENTS   (United States)

^b PHILIPS RESEARCH LABORATORIES   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134572     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400000268     Document Type: Article

References (35)

1. Aihara, K. et al. [1990] "Chaotic neural networks," Phys. Lett. A144, 333-337.
2. Arena, P., Baglio, S., Fortuna, L. & Manganaro, G. [1995] "Simplified scheme for realisation of Chua oscillator by using SC-CNN cells," Electron. Lett. 31(21), 1794-1795.
3. Budinich, M. [1996] "Neural networks for NP-complete problems," in World Congress in Nonlinear Analysis, Athens, Greece.
4. Chakraborty, M. & Chakraborty, U. K. [1997] "Applying genetic algorithm and simulated annealing to a combinatorial optimization problem," Proc. IEEE Int. Conf. Information, Communications and Signal Processing (ICICS'97), Vol. 2, pp. 929-933.
5. Chao, H. et al. [1994] "Neuron design and stability analysis of neural networks for TSP," Proc. IEEE Int. Conf. Systems, Man and Cybernetics, Vol. 3, pp. 2453-2458.
6. Chen, L. [1993] "Application of chaotic simulation and self-organizing neural net to power system voltage stability monitoring," Proc. Second Int. Forum on Applications of Neural Networks to Power Systems (ANNPS'93), pp. 367-372.
7. Chen, L. & Aihara, K. [1995] "Chaotic simulated annealing by a neural-network model with transient chaos," Neural Networks 8(6), 915-930.
8. Chen, L. & Aihara, K. [1995] "Chaotic simulated annealing by a neural network model with transient chaos," Neural Networks 8(6), 915-930.
9. Chen, L. & Aihara, K. [1997] "Chaos and asymptotical stability in discrete-time neural networks," Physica 104, 286-325.
10. Chen, L. & Aihara, K. [1997] "Combinatorial optimization by chaotic dynamics," Proc. IEEE Int. Conf. Systems, Man and Cybernetics, Vol. 3, pp. 2921-2926.
11. Choy, C. S.-T. & Siu, W.-C. [1995] "New approach for solving the travelling salesman problem using self-organizing learning," Proc. IEEE Int. Conf. Neural Networks, Vol. 5, pp. 2632-2635.
12. Durbin, R. & Willshaw, D. [1987] "An analogue approach to the travelling salesman problem using an elastic net method," Nature 326, 689-691.
13. Endo, T., Chua, L. O. & Takeyama, K. [1991] "A neural network using oscillators," Proc. IEEE Int. Symp. Circuits and Systems 1991, Vol. 2, pp. 782-785.
14. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
15. Hasegawa, M., Ikeguchi, T. & Aihara, K. [1996] "Solving traveling salesman problems using a heuristic method with chaotic neuro dynamics," Int. Symp. Non-linear Theory and its Applications (NOLTA'96), pp. 337-340.
16. Hasegawa, M., Ikeguchi, T., Matozaki, T. & Aihara, K. [1995] "Solving combinatorial optimization problems by nonlinear neural dynamics," Proc. 1995 IEEE Int. Conf. Neural Networks (ICNN'95), Vol. 6, pp. 3140-3145.
17. Hayes, S. & Grebogi, C. [1993] "Coding information in the natural complexity of chaos," SPIE 2038, Chaos in Communications, pp. 153-161.
18. Hayes, S., Grebogi, C. & Ott, E. [1993] "Communicating with chaos," Phys. Rev. Lett. 70(20), 3031-3034.
19. Hopfield, J. J. & Tank, D. W. [1985] "Neural computation of decisions in optimization problems," Biol. Cybern. 52, 141-152.
20. Hueter, G. J. [1998] "Solution of the traveling salesman problem with an adaptive ring," Proc. IEEE Int. Conf. Neural Networks, Vol. 1, pp. 85-92.
21. Kanou, N. & Horio, Y. [1995] "Switched-current chaotic neural network with chaotic simulated annealing," Proc 1995 IEEE Int. Conf. Neural Networks (ICNN'95), Vol. 6, pp. 3146-3149.
22. Kaszkurewicz, E. & Bhaya, A. [1994] "On a class of globally stable neural circuits," IEEE Trans. Circuits Syst. I 41(2), 171-174.
23. Kirkpatrick, S., Gelatt, Jr., C. D. & Vecchi, M. P. [1983] "Optimization by simulated annealing," Science 220, 671-680.
24. Lau, K. M., Chan, S. M. & Xu, L. [1995] "Comparison of the Hopfield scheme to the hybrid of Lagrange and transformation approaches for solving the traveling salesman problem," Proc. IEEE Int. Symp. Intelligence in Neural and Biological Systems, pp. 209-216.
25. Madan, R. N. (ed.) [1993] Chua's Circuit A Paradigm for Chaos (World Scientific, Singapore).
26. Matsuyama, Y. [1990] "Competitive self-organization and combinatorial optimization," Int. Joint Conf. Neural Networks, Vol. III, pp. 819-824.
27. Ogorzalek, M. J. [1993] "Taming Chaos - Part I & II," IEEE Trans. Circuits Syst. I 40(10), 693-706.
28. Parker, T. S. & Chua, L. O. [1987] "Chaos: A tutorial for engineers," Proc. IEEE 75(8), 982-1008.
29. Saab, Y. G. & Rao, V. B. [1991] "Combinatorial optimization by stochastic evolution," IEEE Trans. Computer-Aided Design 10(4), 525-535.
30. Sinha, S. & Ditto, W. L. [1998] "Dynamics based computation," Phys. Rev. Lett. 81(10), 2156-2159.
31. Tachibana, Y. et al. [1995] "A simple steepest descent method for minimizing Hopfield energy to obtain optimal solution of the TSP with reasonable certainty," Proc. IEEE Int. Conf. Neural Networks, Vol. 4, pp. 1871-1875.
32. Thiran, P. & Hasler, M. [1994] "Information processing using stable and unstable oscillations: A tutorial," Third IEEE Int. Workshop on CNNs and their Applications (CNNA-94), pp. 127-136.
33. Tomikawa, Y. & Nakayama, K. [1995] "Convergence analysis of recurrent neural network with selfloops based on eigenvalues of a connection matrix," Proc. IEEE Int. Conf. Neural Networks, Vol. 5, pp. 2642-2647.
34. Wang, L. & Smith, K. [1998] "Chaos in the discretized analog Hopfield neural network and potential applications to optimization," Proc. IEEE Int. Conf. Neural Networks, Vol. 2, pp. 1679-1684.
35. Yagiura, M. & Ibaraki, T. [1996] "Metaheuristics as robust and simple optimization tools," Proc. IEEE Int. Conf. Evolutionary Computation, pp. 541-546.