A simulation-supported thought experiment for measuring low-dimensional chaotic systems subjected to parameter drift

We argue that a physics experiment with systems involving drifting parameters requires a paradigm shift: the measured signal, a curve, should be compared with a band resulting from simulations. Based on earlier theoretical results, an accurate description of drifting dissipative chaotic systems can only be given by following an ensemble of trajectories. After convergence to a time-dependent attractor (to the so-called snapshot attractor), the ensemble faithfully represents the dynamics. We point out that an experimentally measured signal should wander within the spread of the converged numerical ensemble, i.e., to behave as any of the ensemble members on the snapshot attractor. If that is the case, the model (a set of ordinary differential equations) used for the simulation can be considered credible. The transient period preceding the arrival to the attractor can be divided into two phases when using two initially localized ensembles. In the first one, a quick spread of the ensembles takes place, and a plume diagram evolves. The next, intermediate phase corresponds to a convergence of the no longer localized ensembles to the same unique time-dependent attractor and lasts approximately as long as the averages and other statistical moments of the two ensembles remain distinct.