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

Yaghi, Shouhei; Shimizu, Toshihiro
June 2000
AIP Conference Proceedings;2000, Vol. 519 Issue 1, p359
Academic Journal
An integration of a deterministic Langevin type equation, driven by a chaotic force, is discussed: ...(t) = x(t) - x(t)² + x(t)ƒ[sub c](t). The chaotic force ƒ[sub c](t) defined by ƒ[sub c](t) = (K/ √τ)...k (y0) for kτ < t Le; (k + 1)τ, (k = 0,1,2, &helip;), where yk is a chaotic sequence of a map F(yk): yk+1 = F(yk). The deviation ...k is Yk - 〈Yo〉, where 〈&helip〉 means the average over the invariant density P (y[sub 0}) 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 ƒ[sub c](t).


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