General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems

被引：78

作者：

Leonov, G. A. ^{[1
,2
]}

机构：

[1] St Petersburg State Univ, St Petersburg 198504, Russia

[2] Harbin Inst Technol, Harbin 150001, Peoples R China

来源：

PHYSICS LETTERS A | 2012年 / 376卷 / 45期

关键词：

Homoclinic trajectory; Fishing principle; Lorenz system; Shimizu-Morioka system; Lu system; Chen system;

D O I：

10.1016/j.physleta.2012.07.003

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The general method for proving the existence of homoclinic trajectories in dissipative systems is developed. The applications of this method to Lorenz-like systems: Lorenz, Shimizu-Morioka, Lu and Chen systems are demonstrated. A criterion for the existence of a homoclinic trajectory within a given family of differential equations (Fishing principle) is presented. New numerical algorithm for the approximation of a homoclinic point in parameters space is constructed. The comparison with Kaplan-Yorke and Shilnikov results is made. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：3045 / 3050

页数：6

共 20 条

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