MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Effects of bounded random perturbations on discrete dynamical systems

Christian S. Rodrigues, Alessandro P.S. de Moura and Celso Grebogi


In this chapter we discuss random perturbations and their effect on dynamical systems. We focus on discrete time dynamics and present different ways of implementing the random dynamics, namely the dynamics of random uncorrelated noise and the dynamics of random maps. We discuss some applications in scattering and in escaping from attracting sets. As we shall see, the perturbations may dramatically change the asymptotic behaviour of these systems. In particular, in randomly perturbed non-hyperbolic scattering trajectories may escape from regions where otherwise they are expected to be trapped forever. The dynamics also gains hyperbolic-like characteristics. These are observed in the decay of survival probability as well as in the fractal dimension of singular sets. In addition, we show that random perturbations also trigger escape from attracting sets, giving rise to transport among basins. Along the chapter, we motivate the application of such processes. We finish by suggesting some possible further applications.

05.45.Ac, 61.43.Hv, 02.50.Ey
Dynamical Systems, random perturbation, stochastic stability

Related publications

2013 Repository Open Access
Christian S. Rodrigues, Alessandro P. S. De Moura and Celso Grebogi

Effects of bounded random perturbations on discrete dynamical systems

In: Bounded noises in physics, biology, and engineering / Alberto D'Onofrio (ed.)
New York : Springer, 2013. - pp. 151-168
(Modeling and simulation in science, engineering and technology)