Abstract
A new noise effect on chaos in one-dimensional mappings is reported. The transition from chaotic behavior to ordered behavior induced by external noise is observed in a certain class of one-dimensional mappings. This transition is clearly shown in terms of the Lyapunov number, entropy, power spectrum, and the nature of orbits.
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G. Mayer-Kress and H. Haken,J. Stat. Phys. 26:149 (1981).
J. P. Crutchfield, J. D. Farmer, and B. A. Huberman, preprint.
K. Tomita and I. Tsuda,Prog. Theor. Phys. 64:1138 (1980).
R. M. May,Nature 261:459 (1976).
R. Bowen,Comm. Math. Phys. 69:1 (1979); S. Ito and Y. Takahashi,J. Math. Soc. Japan 26:33 (1974).
M. Jacobson,Comm. Math. Phys. 81:31 (1981).
C. E. Shannon and W. Weaver,The Mathematical Theory of Communication (Illinois Press, Urbana, 1949); A. I. Khinchin,Mathematical Foundation of Information Theory (Dover, New York, 1957).
G. Bennetin, L. Galgani, and J. Strelcyn,Phys. Rev. A14:2338 (1976).
R. Landauer and J. A. Swanson,Phys. Rev. 121:1668 (1961).
Y. Aizawa,Suppl. Prog. Theor. Phys. 64:491 (1978).
L. D. Landau,Phys. Z. Sowjet. 11:26, 545 (1937).
J. L. Hudson and J. C. Mankin,J. Chem. Phys. 74:6171 (1981).
J. C. Roux, A. Rossi, S. Bachelart, and C. Vidal,Physica 2D:395 (1981); J. C. Roux, J. S. Turner, W. D. McCormick, and H. L. Swinny, inNonlinear Problems; Present and Future, Proceedings of a Conference at Los Alamos, A. R. Bishop, ed. (North-Holland, Amsterdam, 1981).
I. Tsuda and K. Tomita, inNonequilibrium Statistical Physics Problems in Fusion Plasmas -Stochasticityand Chaos—Proceedings of US-Japan Workshop (1981), p. 131.
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In our opinion, the new phenomenon which is reported in this paper may be called “periodicity.” However, we here call this simply “order,” following the comment of one of the referees, because the theory that is expected to justify our opinion is not yet completed. The theory based on the global analysis of maps will be completed in the near future.
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Matsumoto, K., Tsuda, I. Noise-induced order. J Stat Phys 31, 87–106 (1983). https://doi.org/10.1007/BF01010923
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DOI: https://doi.org/10.1007/BF01010923