Shil´nikov´s theorem-a tutorial

Author

Silva, Christopher P.

Author_Institution

Electron. & Sensors Div., Aerosp. Corp., Los Angeles, CA, USA

Volume

40

Issue

10

fYear

1993

fDate

10/1/1993 12:00:00 AM

Firstpage

675

Lastpage

682

Abstract

The phenomenon of chaos has been observed in many nonlinear deterministic systems in both experimental and computer-simulation contexts. Given the nature of this phenomenon, however, an analytical tool is needed to ensure that what is observed is not an artifact of the device used to measure or simulate the given system. This paper provides a tutorial look at one of the few and most useful of such tools: Shil´nikov´s theorem and its various extensions. This exposition presents the basic terminology and concepts related to Shil´nikov´s results, a formal statement and subsequent discussion of its two basic versions for 3D systems, as well as two example applications of Shil´nikov´s method to a piecewise-linear system

Keywords

chaos; multidimensional systems; nonlinear dynamical systems; piecewise-linear techniques; 3D systems; Shil´nikov´s theorem; chaos; nonlinear deterministic systems; piecewise-linear system; Aerodynamics; Analytical models; Chaos; Circuits; Computational modeling; Computer simulation; Differential equations; Orbits; Terminology; Tutorial;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.246142

Filename

246142