Common chaos in arbitrarily complex feedback networks

Physical Review Letters

Volumn 79, Issue 4, 1997, Pages 653-656

  Mestl, Thomas ^a   Bagley, R J ^a   Glass, Leon ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; RANDOM PROCESSES; STATISTICAL METHODS; SWITCHING NETWORKS;

FEEDBACK NETWORKS; RANDOM TELEGRAPH SIGNAL;

CHAOS THEORY;

EID: 7044286330     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.79.653     Document Type: Article

References (40)

1. W. Keister, A. E. Ritchie, and S. H. Washburn, The Design of Switching Circuits (D. Van Nostrand, Toronto, 1951)
2. S. H. Unger, The Essence of Logic Circuits (IEEE Press, Piscataway, New Jersey, 1997), 2nd ed.
3. W. S. McCulloch and W. Pitts, Bull. Math. Biophys., 5, 115 (1943)
4. J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A., 79, 2254 (1982) PNASA6
5. S. A. Kauffman, J. Theor. Biol., 22, 437 (1969).
6. S. A. Kauffman, Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, Oxford, 1993)
7. B. Derrida and Y. Pomeau, Europhys. Lett., 1, 45 (1986).
8. B. Derrida and Y. Pomeau, Europhys. Lett., 2, 739 (1986).
9. B. Luque and R. V. Solé, Phys. Rev. E, 55, 257 (1997) PLEEE8
10. S. Grossberg, Proc. Natl. Acad. Sci. U.S.A., 58, 1329 (1967).
11. L. Glass, J. Chem. Phys., 63, 1325 (1975) JCPSA6
12. L. Glass and J. Pasternack, J. Math. Biol., 6, 207 (1978).
13. J. J. Hopfield Proc. Natl. Acad. Sci. U.S.A., 81, 3088 (1984).
14. R. Thomas and R. D. Àri, Biological Feedback (CRC Press, Boca Raton, 1990)
15. T. Mestl, E. Plahte, and S. W. Omholt, J. Theor. Biol., 176, 291 (1995).
16. T. Mestl, E. Plahte, and S. W. Omholt, Dyn. Stab. Syst., 2, 179 (1995)
17. K. E. Kürten and J. W. Clark, Phys. Lett., 114A, 413 (1986).
18. T. B. Kepler, S. Datt, R. B. Meyer, and L. F. Abbott, Physica (Amsterdam), 46D, 449 (1990).
19. H. Sompolinsky, A. Crisanti, and H. J. Sommers, Phys. Rev. Lett., 61, 259 (1988).
20. J. E. Lewis and L. Glass, Int. J. Bifurcation. Chaos and Sci. Eng., 2, 477 (1991)
21. J. E. Lewis and L. Glass, Neural Comput., 4, 621 (1992).
22. P. K. Das II, W. C. Schieve, and Z. Zeng, Phys. Lett. A, 161, 60 (1991).
23. J. E. Moreira and J. S. Andrade, Jr., Physica (Amsterdam), 206A, 271 (1994).
24. T. Mestl, C. Lemay, and L. Glass, Physica (Amsterdam), 98D, 35 (1996).
25. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, England, 1993), Chap. 4.
26. G. W. Kenrick, Philos. Mag. 7, 176 (1929) PHMAA4
27. S. O. Rice, Bell Syst. Tech. J., 23, 282 (1945).
28. S. Machlup, J. Appl. Phys., 3, 341–343 (1954).
29. Y. Wang, J. Appl. Phys., 74, 15 (1993).
30. C. W. Helstrom, Probability and Stochastic Processes for Engineers (Collier Macmillan, Toronto, 1990).
31. W. M. Wonham and A. T. Fuller, J. Electron. Control, 4, 567 (1958)
32. W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology (Springer-Verlag, Berlin, 1984)
33. P. Ehrenfest and T. Ehrenfest, Phys. Z., 8, 311 (1907).
34. K. W. F. Kohlrausch and E. Schrödinger, Phys. Z., 27, 306 (1926).
35. M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys., 17, 323 (1945).
36. M. Kac, Am. Math. Monthly, 54, 369 (1947)
37. W. Feller, An Introduction to Probability Theory and Its Applications (John Wiley & Sons, London, 1966), Vol. 1, p. 343
38. J.-M. Flesselles and R. Botet, J. Phys. A, 22, 903 (1989) JPHAC5
39. J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West, Fractal Physiology (Oxford University Press, New York, 1994)
40. B. D. Hughes, Random Walks and Random Environments (Clarendon Press, Oxford, 1995), Vol. 1