On the Chaotic Behaviour of Discontinuous Systems

被引：27

作者：

Battelli, Flaviano ^{[1
]}

Feckan, Michal ^{[2
,3
]}

机构：

[1] Univ Politecn Marche, Dipartimento Sci Matemat, I-60131 Ancona, Italy

[2] Comenius Univ, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia

[3] Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2011年 / 23卷 / 03期

关键词：

Bernouilli shift; Chaotic behaviour; Discontinuous systems; EXPONENTIAL DICHOTOMIES; MELNIKOV METHOD; BIFURCATIONS; ORBITS;

D O I：

10.1007/s10884-010-9197-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed discontinuous systems whose unperturbed part has a piecewise C (1) homoclinic solution that crosses transversally the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has solutions that behave chaotically. Application of this result to quasi periodic systems are also given.

引用

页码：495 / 540

页数：46

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