On existence of homoclinic orbits for some types of autonomous quadratic systems of differential equations

被引：12
作者：
Belozyorov, Vasiliy Ye. [1 ]
机构：
[1] Dnepropetrovsk Natl Univ, Phys & Tech Dept, UA-49050 Dnepropetrovsk, Ukraine
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 09期
关键词：
System of ordinary quadratic differential equations; Linear transformation; Boundedness; Negative definiteness; Homoclinic orbit; Chaotic attractor; CHAOTIC ATTRACTOR; LORENZ SYSTEM; BIFURCATION; FEEDBACK; DYNAMICS;
D O I：
10.1016/j.amc.2010.11.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The new existence conditions of homoclinic orbits for the system of ordinary quadratic differential equations are founded. Further, the realization of these conditions together with the Shilnikov Homoclinic Theorem guarantees the existence of a chaotic attractor at 3D autonomous quadratic system. Examples of the chaotic attractors are given. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：4582 / 4595
页数：14
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