ON THE INFLUENCE OF NOISE ON THE LARGEST LYAPUNOV EXPONENT AND ON THEGEOMETRIC STRUCTURE OF ATTRACTORS

In this paper we present an overview of a classification of alternativ e mathematical schemes which determine possible impositions of noise o n dynamic systems either of a continuous or discrete formulation in ti me; see [1]. When a noise interferes with the evolution of a dynamic s ystem it is called a dynamic noise. Such a dynamic noise may take the form of an additive or multiplicative expression which illustrate the kind of parameters by which noise may enter into the equations of a dy namic system. We also consider the case of an output noise, i.e. a noi se which does not influence the evolution of a dynamic system. The out put noise is again divided into additive and multiplicative forms, dep ending on how it is introduced into the formulation of the system. We present some numerical investigations concerning the influence of nois e on i) the correlation dimension, ii) the largest Lyapunov exponent a nd iii) the geometric structure of the Henon and Lorenz attractors. We also recall, a method of constructing models for effecting prediction s of time series with a finite correlation dimension as obtained in [1 ]. (C) 1998 Elsevier Science Ltd. All rights reserved.