Relation between Langevin type equation driven by the chaotic force and stochastic differential equation

Details Relation between Langevin type equation driven by the chaotic force and stochastic differential equation Relation between Langevin type equation driven by the chaotic force and stochastic differential equation

Jun 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aipc..519..359y&link_type=abstract

STATISTICAL PHYSICS: Third Tohwa University International Conference. AIP Conference Proceedings, Volume 519, pp. 359-361 (2000

Physics

Stochastic Analysis Methods, Low-Dimensional Chaos, Self-Organized Systems

Scientific paper

An integration of a deterministic Langevin type equation, driven by a chaotic force, is discussed: ẋ(t)=x(t)-x(t)2+x(t)fc(t). The chaotic force fc(t) defined by fc(t)=(K/τ)ŷk(y0) for kτ, where <...> means the average over the invariant density ρ(y0) of F(y). In the small τ limit the result is compared with the result in the stochastic differential equation. The similar results as in the stochastic case are obtained due to the factor 1/τ of the chaotic force fc(t). .

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