Generalized Langevin equation with chaotic force

Toshihiro Shimizu

Physica A: Statistical Mechanics and its Applications, 1994, vol. 212, issue 1, 61-74

Abstract: The generalized Langevin equation with chaotic force is investigated: ẋ(t) = − ∫0tdt′φ(t,t′)x(t′) + ƒ(t), where φ(t,t′) = 《ƒ(t)ƒ(t′) 》《x2 》. The chaotic force ƒ(t) is defined by ƒ(t)=(yn+1 − 《y》τ for nτ < t ≤ (n + 1)τ (n= 0,1,2,…), where yn+1 is a chaotic sequence: yn+1 = F(yn). The time evolution of x(t), which is generated by the chaotic force, is discussed. The approach of the distribution function of x to a stationary distribution is studied. It is shown that the distribution function satisfies the Fokker-Planck type equation with the memory effect in the small τ limit. The relation between the invariant density of F (y) and the stationary distribution of x is discussed.

Date: 1994
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437194901376
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:212:y:1994:i:1:p:61-74

DOI: 10.1016/0378-4371(94)90137-6

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().