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.
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页码：495 / 540
页数：46
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