Collapsing effects in numerical simulation of a class of chaotic dynamical systems and random mappings with a single attracting centre

Abstract

Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic replaces continuum state spaces. In some circumstances, complicated theoretical behaviour has a tendency to collapse to trivial and degenerate behaviour as a result of discretizations. Characteristics of such collapsing effects often seem to depend on the corresponding discretization only in a random way. We describe a procedure to construct a stochastic process with similar statistical characteristics. Results of computer modelling are discussed.