In this paper we use discrete dynamical systems formalism to carefully investigate the effect of a time-dependent perturbation on a classical mechanical model. We present a study of a one-dimensional Fermi accelerator model and its parametric dependence on the amplitude of the movement of the...

Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling...

We study numerically the dynamical behavior of a classical particle inside a box potential that contains a square well which depth varies in time. Two cases of time dependence are investigated: periodic and stochastic. The periodic case is similar to the one-dimensional Fermi accelerator model,...

We propose a novel methodology for forecasting chaotic systems which is based on exploiting the information conveyed by the local Lyapunov ex- ponent of a system. We show how our methodology can improve forecast- ing within the attractor and illustrate our results on the Lorenz system.