We introduce a scale dependent stability number which describes the response of a dynamical system to finite size perturbations. By construction, it converges to the maximal Lyapunov exponent in the limit of infinitesimal perturbations. We discuss different dynamical systems which are linearly stable but unstable in terms of the finite size analysis. In such a situation typical trajectories can show temporal disorder, which has its origin in a kind of mixing on the mesoscopic scales.

• Received 17 August 1999

DOI:https://doi.org/10.1103/PhysRevE.61.2533