On the relation between reliable computation time, float-point precision and the Lyapunov exponent in chaotic systems

Abstract

The relation among reliable computation time, Tc, float-point precision, K, and the Lyapunov exponent, λ, is obtained as Tc= (lnB/λ)K+C, where B is the base of the float-point system and C is a constant dependent only on the chaotic equation. The equation shows good agreement with numerical experimental results, especially the scale factors.

8 pages

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