Prog. Theor. Phys. Vol. 68 No. 2 (1982) pp. 665-668

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Letters

Relaxation of Systems under the Effect of a Colored Noise

— Exactly Soluble Models —

Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812
^*Faculty of Liberal Arts, Shizuoka University, Shizuoka 422

(Received March 29, 1982)

Abstract:

Exact and explicit results are obtained for the relaxation of a wide class of nonlinear systems under the effect of a colored noise. A critical slowing down is shown to appear under a condition for a class of model systems. Its white noise limit is also discussed.

URL : http://ptp.ipap.jp/link?PTP/68/665/
DOI : 10.1143/PTP.68.665

References:

For reviews, see for example
L. Arnold and R. Lefever, editors, Stochastic Nonlinear Systems in Physics, Chemistry and Biology (Springer, Berlin, 1981).
M. Slatkin, Ecology 59 (1978), 249.
K. Kitahara, W. Horsthemke, R. Lefever and Y. Inaba, Prog. Theor. Phys. 64 (1980), 1233[PTP].
H. Matsuda and K. Ishii, J. Math. Boil. 11 (1981), 119.
W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2 (John Wiley, New York, 1966), chap. X.
G. C. Papanicolaou, Bull. Amer. Math. Soc. 81 (1975), 330.
R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1 (Interscience, New York, 1953), p. 354.
K. Ishii and K. Kitahara, in preparation.
G. Doetsch, Handbuch der Laplace-Transformation, Band I. (Birkhauser, Basal, 1971), S. 498.
A. Schenzle and H. Brand, Phys. Rev. A 20 (1979), 1628[APS].
L. Brenig and N. Banai, Physica D 5, 208[CrossRef].
M. Suzuki, K. Kaneko and S. Takesue, Prog. Theor. Phys. 67 (1979), 1756[PTP].
M. Suzuki, S. Takesue and F. Sasagawa, Prog. Theor. Phys. 68 (1979), 98[PTP].

Citing Article(s) :

Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 1917-1934 :
Universality and Scaling Law of Long-Time Tails in Multiplicative Stochastic Processes

Masuo Suzuki
Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 790-800 :
Critical Slowing Down in Random Growing-Rate Models with General Two Level Markov Noise

Fumiyoshi Sasagawa
Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 312-314 :
Relaxation of Systems under the Effect of a Gaussian White Noise

Kazuo Kitahara and Kazushige Ishii
Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1255-1257 :
On the Influence of Weak Additive Noise on the Long Time Behaviour of the Correlation Functions for Multiplicative Stochastic Processes

H. R. Brand
Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1013-1021 :
Monte Carlo Simulation of Nonlinear Stochastic Processes

Fumiyoshi Sasagawa, Seiji Miyashita and Masuo Suzuki

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