On Reliable Computation of Lifetime in Transient Chaos

Abstract

Transient chaos is typical behavior of dynamical systems. The computation of lifetimes is a significant task in transient chaos and relates to many applications, such as finding a long-lived trajectory to approximate chaotic saddle in high precision or controlling of transient chaos. However, the lifetime of a single initial point may vary drastically when computed with different numerical setups, indicating that the computed lifetime is likely to be incorrect. In this paper, the Lorenz equation is used as a benchmark to study the computation of lifetimes with a new numerical strategy, namely the Clean Numerical Simulation (CNS). We illustrate that the lifetime can only be computed reliably by the CNS. The mechanism of the imprecision of lifetime computed with traditional numerical methods is also analyzed via numerical experiments. In addition, the computation of long-lived trajectories is studied as an example to explain why reliable computation of lifetimes is crucial.