Chemistry and Physics Faculty Articles

Title

Characterization of the Rossler System in Parameter Space

Document Type

Article

Publication Date

3-2007

Publication Title

International Journal of Bifurcation and Chaos

Keywords

Rössler system, Lyapunov exponent values, Swallows

ISSN

0218-1274

Volume

17

Issue/No.

3

First Page

965

Last Page

973

Abstract

We characterize the Rössler system by means of a map associating colors to various intervals of largest Lyapunov exponent values in parameter space. This color map allows quick access to quantitative information about the dynamics of the system. The map also permits parameter space navigation while intentionally maintaining the system in a desired state, and avoiding regions where the system's behavior would be undesirable. In addition, the map exhibits a rich structure of stability clusters composed of affine-similar repetitions of basic elementary cells called "swallows." These cells, until recently, have been known to be associated with discrete maps only.

DOI

10.1142/S0218127407017689

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Peer Reviewed

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