Dependence of lifetimes of chaotic transients in the weakly dissipative Duffing oscillator on numerical precision and external noise

A numerical experiment was performed for a distribution of lifetimes of chaotic transients in the weakly dissipative single-well Duffing oscillator. It is shown that the results of computations with a uniform distribution of precision of numerical algorithm at a fixed initial condition cannot be distinguished from the well-known exponential distribution of lifetimes computed with an uniform distribution of initial conditions at fixed numerical precision. The same exponential distribution of lifetimes is also obtained if a noise term is added to the driving force in the fixed precision case.