A STATISTICAL METHOD FOR DETECTING CYCLES IN DISCRETE DYNAMICAL SYSTEMS

Abstract

This paper introduces a statistical method for detecting cycles in discrete time dynamical systems. The continuous state space is replaced by a discrete one consisting of cells. Hashing is used to represent the cells in the computer’s memory. An algorithm for a two-parameter bifurcation analysis is presented which uses the statistical method to detect cycles in the discrete state space. The output of this analysis is a colored cartogram where parameter regions are marked according to the long-term behavior of the system. Moreover, the algorithm allows the computation of basins of attraction of cycles.