The mathematical theory of chaos

Document Type

Article

Publication Date

1-1-1986

Abstract

The basic concepts of the mathematical theory of chaos are presented through a brief analysis of some interesting dynamical systems in one-, two- and three-dimensional space. We start with a discussion of interval maps and observe that when such maps are monotonic, their iterates behave in an orderly fashion. Then, by way of contrast, we study a well-known quadratic1 map iterates clearly manifest the archetypal characteristics of chaos, such as period-doubling bifurcations and the existence of a strange attractor. As a means of indicating that mappings in two dimensions yield a richer variety of chaotic regimes than do interval maps, we next discuss the horseshoe and solenoidal mappings of the two-disk. Dizzying forms of chaos emerge from these mappings, but there is an irony-the chaotic behavior can be characterized in an orderly way. We conclude with a cursory examination of the Lorenz differential equation in three-space: a primary source of the recent interest in chaos theory. © 1986.

Identifier

33645649162 (Scopus)

Publication Title

Computers and Mathematics with Applications

External Full Text Location

https://doi.org/10.1016/0898-1221(86)90439-6

ISSN

08981221

First Page

1039

Last Page

1045

Issue

3-4 PART 2

Volume

12

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