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

The relation among reliable computation time, Tc, float-point precision, K, and the Lyapunov exponent, {\lambda}, is obtained as Tc= (lnB/{\lambda})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.