Chaotic Behavior and Strange Attractors in Dynamical Systems

Abstract

In this paper, we study the invariant set of dynamical systems in which attractor and non-attractor sets exist. We aim to carve out a small section of the theory of chaotic dynamical systems-that of attractors-and outline its fundamental concepts from a computational mathematics perspective. The motivation for this paper is primarily to define what an attractor is and to clarify what distinguishes its various types (non-strange, strange non-chaotic, and strange chaotic). We discuss the Hénon and Lorenz attractors as important examples of this type of chaotic system.