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MiS Preprint
35/2012

Effects of bounded random perturbations on discrete dynamical systems

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

Abstract

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.

Received:
Jun 22, 2012
Published:
Jun 22, 2012
PACS:
05.45.Ac, 61.43.Hv, 02.50.Ey
Keywords:
Dynamical Systems, random perturbation, stochastic stability

Related publications

inBook
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)