Edge of chaos and local activity domain of FitzHugh-Nagumo equation

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 2, 1998, Pages 211-257

  Dogaru, Radu ^a,b   Chua, Leon O ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY POLITEHNICA OF BUCHAREST   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032008348     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498000152     Document Type: Article

References (27)

1. Bronshtein, I. N. & Semendyayev, K. A. [1985] Handbook of Mathematics (English translation), (Van Nostrand Reinhold Company, New York), p. 119.
2. Chua, L. O. [1980] "Dynamic nonlinear networks: State of the art," IEEE Trans. Circuits Syst. 27(11), 1059-1087.
3. Chua, L. O., Desoer, C. A. & Kuh, E. A. [1985] Linear and Nonlinear Circuits (McGraw Hill, New York).
4. Chua, L. O. & Yang, L. [1988] "Cellular neural networks: Theory and applications," IEEE Trans. Circuits Syst. 35, 1257-1290.
5. 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 42, 559-577.
6. Chua, L. O. [1997] "CNN: A vision of complexity," Int. J. Bifurcation and Chaos 7(10), 2219-2425.
7. Cronin, J. [1987] Mathematical Aspects of Hodgkin-Huxley Neural Theory (Cambridge University Press, Cambridge).
8. Crounse, K. R. & Chua, L. O. [1996] "The CNN universal machine is as universal as Turing machine," IEEE Trans. Circuits Syst. 43(4), 353-355.
9. Dogaru, R. & Chua, L. O. [1998] "Rectification neural networks: A novel adapative architecture and its application for implementing the local logic of cellular neural networks," U. C. Berkeley, Electronics Research Laboratory Memorandum No. UCB/ERL M98/4, 15 January 1998.
10. FitzHugh, R. [1969] "Mathematical models of excitation and propagation nerve," in Biological Engineering, ed. Schwan, H. (McGraw-Hill, New York), pp. 1-85.
11. Forrest, S. [1990] "Emergent computation: Self-organizing, collective, and cooperative phenomena in natural and artificial computing networks," Physica D42, 1-11.
12. Haken, H. [1994] "Synergetics: From pattern formation to pattern analysis and pattern recognition," Int. J. Bifurcation and Chaos 4(5), 1069-1083.
13. Hartman, P. [1982] Ordinary Differential Equations (Birkhäuser, Boston).
14. Jahnke, W & Winfree, A. T. [1991] "A survey of spiral-wave behaviors in the oregonator model," Int. J. Bifurcation and Chaos 2, 445-466.
15. Kauffman, S. A. [1993] The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, New York).
16. Kauffman, S. A. [1995] At Home in the Universe: The Search for Laws of Self-Organization and Complexity (Oxford University Press).
17. Langton, C. G. [1990] "Computation at the edge of chaos: Phase transitions and emergent computation," Physica D42, 12-37.
18. Mitchell, M., Crutchfield, J. P. & Hraber, P. T. [1993] "Dynamics, computation, and the 'edge of chaos': A re-examination," Santa Fe Institute Working Paper 93-06-040.
19. Murray, J. D. [1989] Mathematical Biology (Springer-Verlag, Berlin).
20. Muñuzuri, A. P., Pérez-Muñuzuri, V., Gómez-Gesteira, M., Chua, L. O. & Pérez-Villar, V. [1995] "Spatiotemporal structures in discretely-coupled arrays of nonlinear circuits: A review," Int. J. Bifurcation and Chaos 5(1), 17-50.
21. Nicolis, G. & Prigogine, I. [1989] Exploring Complexity (W. H. Freeman, New York).
22. Packard, N. [1988] "Adaptation toward the edge of chaos," Center for Complex Systems Research Technical Report, University of Illinois, CCSR-88-5.
23. Prigogine, I. [1980] From Being to Becoming: Time and Complexity in the Physical Sciences (W. H. Freeman, San Francisco).
24. Roska, T. & Chua, L. O. [1993] "The CNN universal machine: an analogic array computer," IEEE Trans. Circuits Syst. II: Analog and Digital Signal Processing 40, 163-173.
25. Schrödinger, E. [1967] What is Life? The Physical Aspect of the Living Cell & Mind and Matter (University Press, Cambridge).
26. Toffoli, T. & Margolis, N. [1987] Cellular Automata Machines (The MIT Press, Cambridge, MA).
27. Wolfram, S. [1984] "Universality and complexity in cellular automoata," Physica D10, 1-35.