Physics – Condensed Matter
Scientific paper
1995-02-22
Physics
Condensed Matter
uuencoded gzipped .tar file with 9 pages of .ps file and 2 .ps figures
Scientific paper
10.1088/0305-4470/29/10/009
We discuss the predictability of a conservative system that drives a chaotic system with positive maximum Lyapunov exponent $\lambda_0$, such as the erratic motion of an asteroid in the gravitational field of two bodies of much larger mass. We consider the case where in absence of feedback (restricted model), the driving system is regular and completely predictable. A small feedback of strength $\epsilon$ still allows a good forecasting in the driving system up to a very long time $T_p \sim \epsilon^{-\alpha}$, where $\alpha$ depends on the details of the system. The most interesting situation happens when the Lyapunov exponent of the total system is strongly chaotic with $\lambda_{tot} \approx \lambda_0$ , practically independent of $\epsilon$. Therefore an exponential amplification of a small incertitude on the initial conditions in the driving system for any $\epsilon \neq 0$ coexists with very long predictability times. The paradox stems from saturation effects in the evolution for the growth of the incertitude as illustrated in a simple model of coupled maps and in a system of three point vortices in a disk.
Boffetta Guido
Paladin Giovanni
Vulpiani Angelo
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