Calculation of homoclinic and heteroclinic orbits in 1D maps

被引：8

作者：

Avrutin, Viktor ^{[1
,3
]}

Schenke, Bjoern ^{[2
]}

Gardini, Laura ^{[3
]}

机构：

[1] Univ Stuttgart, IST, Stuttgart, Germany

[2] Univ Stuttgart, IPVS, Stuttgart, Germany

[3] Univ Urbino, DESP, I-61029 Urbino, Italy

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2015年 / 22卷 / 1-3期

关键词：

Homoclinic orbits; Heteroclinic connections; Algorithms; Homoclinic and heteroclinic bifurcations; Piecewise smooth maps; Discontinuous maps; Chaotic attractors; SNAP-BACK REPELLERS; CHAOTIC ATTRACTORS; ROBUST CHAOS; SCENARIO; CRISIS;

D O I：

10.1016/j.cnsns.2014.07.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Homoclinic orbits and heteroclinic connections are important in several contexts, in particular for a proof of the existence of chaos and for the description of bifurcations of chaotic attractors. In this work we discuss an algorithm for their numerical detection in smooth or piecewise smooth, continuous or discontinuous maps. The algorithm is based on the convergence of orbits in backward time and is therefore applicable to expanding fixed points and cycles. For simplicity, we present the algorithm using 1D maps. (C) 2014 The Authors. Published by Elsevier B.V.

引用

页码：1201 / 1214

页数：14

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