Strange Attractors: The Locus of Chaos

Abstract

Having discussed the phenomena of chaos and the routes leading to it in ‘simple’ one-dimensional settings, we continue with the exposition of chaos in dynamical systems of two or more dimensions. This is the relevant case for models in the natural sciences since very rarely can processes be described by only one single state variable. One of the main players in this context is the notion of strange attractors.

Never in the annals of science and engineering has there been a phenomenon so ubiquitous, a paradigm so universal, or a discipline so multidisciplinary as that of chaos. Yet chaos represents only the tip of an awesome iceberg, for beneath it lies a much finer structure of immense complexity, a geometric labyrinth of endless convolutions, and a surreal landscape of enchanting beauty. The bedrock which anchors these local and global bifurcation terrains is the omnipresent nonlinearity that was once wantonly linearized by the engineers and applied scientists of yore, thereby forfeiting their only chance to grapple with reality.

Leon O. Chua¹