Chaotic resonance - Methods and applications for robust classification of noisy and variable patterns

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 6, 2001, Pages 1607-1629

  Kozma, Robert ^a   Freeman, Walter J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040437042     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401002870     Document Type: Article

References (65)

1. Aihara, K., Takabe, T. & Toyoda, M. [1990] "Chaotic neural networks," Phys. Lett. A144(6&7), 333-340.
2. Amari, S. [1977] "Neural theory of association and concept formation," Biol. Cybern. 26, 175-185.
3. Anderson, J. A., Silverstein, J. W., Ritz, S. A. & Jones, R. S. [1977] "Distinctive features, categorical perception, and probability learning: Some applications of a neural model," Psychol. Rev. 84, 413-451.
4. Andreyev, Y. V., Dmitriev, A. S. & Kuminov, D. A. [1996] "1-D maps, chaos and neural networks for information processing," Int. J. Bifurcation and Chaos 6(4), 627-646.
5. Aradi, I., Barna, G. & Erdi, P. [1995] "Chaos and learning in the olfactory bulb," Int. J. Intell. Syst. 10(1), 89-117.
6. Barrie, J. M., Freeman, W. J. & Lenhart, M. D. [1996] "Statiotemporal analysis of prepyriform, visual, auditory, and somesthetic surface EEGs in trained rabbits," J. Neurophysiol. 76(1), 520-539.
7. Borisyuk, R. M. & Borisyuk, G. N. [1997] "Information coding on the basis of synchronization of neuronal activity," Biosyst. 40(1&2), 3-10.
8. Brown, R. & Chua, L. [1991] "Horseshoes and the twist- and-flip map," J. Bifurcation and Chaos 1, 235-252.
9. Brown, R. & Chua, L. O. [1999] "Clarifying chaos 3. Chaotic and stochastic processes, chaotic resonance and number theory," Int. J. Bifurcation and Chaos 9, 785-803.
10. Buckley, S. & Stelson, S. [1978] "Phase monitoring for automated inspection, positioning and assembly," Trans. Soc. Manufacturing Engin. 6, 56-63.
11. Carroll, T. L. & Pecora, L. M. [1993] "Stochastic resonance and chaos," Phys. Rev. Lett. 70, 576-579.
12. Chang, H.-J. & Freeman, W. J. [1998] "Biologically modeled noise stabilizing neurodynamics for pattern recognition," Int. J. Bifurcation and Chaos 8(2), 321-345.
13. Chang, H. J., Freeman, W. J. & Burke, B. C. [1998] "Optimization of olfactory model in software to give 1/f power spectra reveals numerical instabilities in solutions governed by aperiodic (chaotic) attractors," Neural Networks 11, 449-466.
14. Chang, H.-J. & Freeman, W. J. [1999] "Local homeostasis stabilizes a model of the olfactory system globally in respect to perturbations by input during pattern classification," Int. J. Bifurcation and Chaos 8, 2107-2123.
15. Chua, L. O., Hasler, M., Moschytz, G. S. & Neirynck, J. [1995] "Autonomous cellular neural networks -A unified paradigm for pattern formation and active wave propagation," IEEE Trans. Circuits Syst. I: Fundamental Th. Appl. 42, 559-577.
16. Dawson, S., Grebogyi, C., Sauer, T. & Yorke, J. A. [1994] "Obstructions to shadowing when a Lyapunov exponent fluctuates about zero," Phys. Rev. Lett. 73, 1927-1930.
17. Ditto, W. L., Rauseo, S. N. & Spano, M. L. [1990] "Experimental control of chaos," Phys. Rev. Lett. 26, 3211-3214.
18. Dogaru, R. & Chua, L. O. [1998] "Edge of chaos and local activity domain of FitzHugh-Nagumo equation," Int. J. Bifurcation and Chaos 8, 211-257.
19. Freeman, W. J. [1975] Mass Action in the Nervous System (Academic Press, NY).
20. Freeman, W. J. [1987] "Simulation of chaotic EEG patterns with a dynamic model of the olfactory system," Biol. Cybern. 56, 139-150.
21. Freeman, W. J. [1988] "Strange attractors that govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential," IEEE Trans. Circuits Syst. 35, 781-783.
22. Freeman, W. J., Yao, Y. & Burke, B. [1988] "Central pattern generating and recognizing in olfactory bulb: A correlation learning rule," Neural Networks 1, 277-288.
23. Freeman, W. J. [1992] "Tutorial on neurobiology - From single neurons to brain chaos," Int. J. Bifurcation and Chaos 2(3), 451-482.
24. Freeman, W. J. [1996] "Random activity at the microscopic neural level in cortex ("noise") sustains and is regulated by low-dimensional dynamics of macroscopic cortical activity ("chaos")," Int. J. Neural Syst. 7, 473-480.
25. Freeman, W. J. [1997] "Il sistema olfattivo: Rilevamento e classificazione degli odori," Chapter in Part 2 of "Frontiere della vita," eds. Amit, D., Parisi, G. Roma: Istituto della Enciclopedia Italiana, Vol. 3, pp. 477-494; The original in English, "Olfactory system: Odor detection and classification" is to be found on http://sulcus.berkeley.edu.
26. Freeman, W. J., Chang, H. J., Burke, B. C., Rose, P. A. & Badler, J. [1997] "Taming chaos: Stabilization of aperiodic attractors by noise," IEEE Trans. Circuits Syst. I: Fundamental Th. Appl. 44(10), 989-996.
27. Freeman, W. J. [1999] "Noise-induced first-order phase transitions in chaotic basin activity," Int. J. Bifurcation and Chaos 9, 2215-2218.
28. Freeman, W. J. [2000a] Neurodynamics: An Exploration of Mesoscopic Brain Dynamics (Springer-Verlag, London, UK).
29. Freeman, W. J. [2000b] "A proposed name for aperiodic brain activity: Stochastic chaos," Neural Networks 13, 11-13.
30. Freeman, W. J. & Barrie, J. M. [2000] "Analysis of spatial patterns of phase in neocortical gamma EEGs in rabbit," J. Neurophysiol. 84, 1266-1278.
31. Freeman, W. J. & Kozma, R. [2000] "Local-global interactions and the role of mesoscopic (intermediate-range) elements in brain dynamics," Behav. Brain Sci. 23(3), 401-432.
32. Fryska, S. T. & Zohdy, M. A. [1992] "Computer dynamics and shadowing of chaotic orbits," Phys. Lett. A166, 340-346.
33. Gammaitoni, L., Hanggi, P., Jung, P. & Marchesoni, F. [1998] "Stochastic resonance," Rev. Mod. Phys. 70(1), 223-287.
34. Grossberg, S. [1980] "How does a brain build a cognitive code?" Psychol. Rev. 87, 1-51.
35. Haken, H. [1983] Synergetics: An Introduction (Springer, Berlin).
36. Hamel, S. M., Yorke, J. A. & Grebogi, C. [1987] "Do numerical orbits of chaotic dynamical processes represent true orbits?" J. Complexity 3, 136-145.
37. Hopfield, J. J. [1982] "Neuronal networks and physical systems with emergent collective computational abilities," Proc. Natl. Acad. Sci. USA 81, 3058-3092.
38. Ishii, S., Fukumizu, K. & Watanabe, S. [1996] "A network of chaotic elements for information processing," Neural Networks 9(1), 25-40.
39. Kaneko, K. [1986] Collapse of Tori and Genesis of Chaos in Dissipative Systems (World Scientific, Singapore).
40. Kaneko, K. [1990] "Clustering, coding, switching, hierarchical ordering and control in network of chaotic elements," Physica D41, 137-142.
41. Kay, L. M. & Freeman, W. J. [1998] "Bidirectional processing in the olfactory-limbic axis during olfactory behavior," Behav. Neurosci. 112, 541-553.
42. Kohonen, T. [1972] "Correlation matrix memories," IEEE Trans. Comput. C-21, 353-359.
43. Konishi, K. & Kokame, H. [1998] "Observer-based delayed-feedback control for discrete-time chaotic systems," Phys. Lett. A248, 359-368.
44. Kozma, R. [1998] "Intermediate range coupling generates low-dimensional attractors deeply in the chaotic region of one-dimensional lattices," Phys. Lett. A244, 85-91.
45. Kozma, R & Freeman, W. J. [1999a] "A possible mechanism for intermittent oscillations in the KIII model of dynamic memories - the case study of olfaction," Proc. Int. Joint Conf. Neural Networks, IJCNN99, Washington D. C., July 10-16, 1999, Vol. 1, pp. 52-57.
46. Kozma, R. & Freeman, W. J. [1999b] "Knowledge acquisition in connectionist systems via crisp, fuzzy and chaos methods," CRC Handbook of Applied Computational Intelligence, to appear.
47. Kozma, R. & Freeman, W. J. [2000] "Encoding and recall of noisy data as spatio-temporal memory patterns in the style of brains," Proc. IEEE Int. Joint Conf. Neural Networks, IJCNN2000, Como, July 24-27, 2000, Vol. 5, pp. 33-38.
48. Liao, T. L. [1998] "Observer-based approach for controlling chaotic systems," Phys. Rev. E57, 1604-1610.
49. Minai, A. A. & Anand, T. [1998] "Stimulus induced bifurcations in discrete-time neural oscillators," Biol. Cybern. 79(1), 87-96.
50. Moss, F. & Pei, X. [1995] "Stochastic resonance -Neurons in parallel," Nature 376, 211-212.
51. Nakagawa, M. [1998] "Chaos associative memory with a periodic activation function," J. Phys. Soc. Japan 67(7), 2281-2293.
52. Pecora, L. M. & Carroll, T. L. [1991] "Pseudoperiodic drifting: Eliminating multipole domains of attraction using chaos," Phys. Rev. Lett. 67, 945-948.
53. Perrone, A. L. & Basti, G. [1995] "Neural images and neural coding," Behav. Brain Sci. 1892, 368-369.
54. Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. & Ditto, W. L. [1994] "Controlling chaos in the brain," Nature 230, 615-620.
55. Schuster, H. G. & Stemmler, M. B. [1997] "Control of chaos by oscillating feedback," Phys. Rev. E56(6), 6410-6417.
56. Shimoide, K. & Freeman, W. J. [1995] "Dynamic neural network derived from the olfactory system with examples of applications," IEICE Trans. Fundamentals E-78A, 869-884.
57. Skarda, C. A. & Freeman W. J. [1987] "How brains make chaos in order to make sense of the world," Behav. Brain Sci. 10, 161-195.
58. Tavares, V. G., Principe, J. C. & Harris, J. G. [2000] "A silicon olfactory bulb oscillator," IEEE Int. Symp. Circuits and Systems, Vol. V, Geneva, Switzerland, pp. 397-400.
59. Tsuda, I. [1992] "Dynamic link of memory - Chaotic memory map in nonequilibrium neural networks," Neural Networks 5, 313-326.
60. Wang, L. P. [1996] "Oscillatory and chaotic dynamics in neural networks under varying operating conditions," IEEE Trans. Neural Networks 7(6), 1382-1388.
61. Werbos, P. J. [1992] "Neurocontrol and supervised learning - an overview and evaluation," in Handbook of Intelligent Control, eds. White, D. A. & Sofge, D. A., pp. 65-89.
62. Wiesenfeld, K. & Hadley, P. [1989] "Attractor crowding in oscillator arrays," Phys. Rev. Lett. 62, 1335-1338.
63. Yao, Y. & Freeman, W. J. [1990] "Model of biological pattern recognition with spatially chaotic dynamics," Neural Networks 3, 153-170.
64. Yao, Y., Freeman, W.J., Burke, B. & Yang, Q. [1991] "Pattern recognition by a distributed neural network: An industrial application," Neural Networks 4, 103-121.
65. Zak, M. [1991] "Terminal chaos for information processing in neurodynamics," Biol. Cybern. 64, 343-351.