Attractor identification and prediction for iterative dynamical systems
Ying Liu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
ABSTRACT There are four algorithms to find an attractor of a contractive iterated function system: iteration algorithm, random algorithm, branch-and-bound algorithm,and adjacency matrix algorithm. In this paper, we will present a new algorithm, thebisection algorithm. 1. INTRODUCTION Dynamical systems can be used to process information. In general, there aretwo approaches: storing information in attractors of dynamical systems and storinginformation in orbits of dynamical systems. In this paper, we will use the approachof information processing using attractors of dynamical systems.The idea of processing information by attractors of dynamical systems wasintroduced by Hopfield in his Hopfield neural network model [11) and by Barnsley in the Fractal data compression (2]. In either case, attractor identification and prediction is a very important subject. Lju has classified dynamical systems inseveral different ways, including classification by attractor topology, by spacecomplexity of parameter space, and by information capacity (6,7]. There are many