SHILNIKOV THEOREM - A TUTORIAL

被引：267

作者：

SILVA, CP ^{[1
]}

机构：

[1] AEROSP CORP,DIV ELECTR & SENSORS,LOS ANGELES,CA 90009

来源：

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS | 1993年 / 40卷 / 10期

关键词：

D O I：

10.1109/81.246142

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

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 3-D systems, as well as two example applications of Shil'nikov's method to a piecewise-linear system.

引用

页码：675 / 682

页数：8

共 7 条

[1] THE DOUBLE HOOK [J].

BARTISSOL, P ;

CHUA, LO .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (12) :1512-1522

[2] THE DOUBLE SCROLL FAMILY .1. RIGOROUS PROOF OF CHAOS [J].

CHUA, LO ;

KOMURO, M ;

MATSUMOTO, T .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1986, 33 (11) :1072-1097

[3]

Shilnikov L.P., 1965, SOV MATH DOKL, V6, P163

[4]

Shilnikov L. P., 1970, MATH USSR SBORNIK, V10, P91

[5]

SMALE S, 1965, DIFFERENTIAL COMBINA, P63, DOI DOI 10.1515/9781400874842-006

[6]

TRESSER C, 1984, ANN I H POINCARE-PHY, V40, P441

[7]

[No title captured]

← 1 →