COLLAPSING EFFECTS IN NUMERICAL SIMULATION OF A CLASS OF CHAOTIC DYNAMICAL SYSTEMS AND RANDOM MAPPINGS WITH A SINGLE ATTRACTING CENTRE

摘要

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. [References: 18]