IJPAM: Volume 36, No. 3 (2007)

SHIL'NIKOV HETEROCLINIC ORBITS
IN A CHAOTIC SYSTEM

Feng Yun Sun$^1$, Yu Qing Yan$^2$
$^{1,2}$School of Mathematics and Computational Science
Zhongshan University
Guangzhou, 510275, P.R. CHINA
$^1$e-mail: hanessfy@yahoo.com.cn
$^2$e-mail: yyqingcxx@yahoo.com.cn


Abstract.In this paper, a chaotic system is considered which exhibits a chaotic attractor with only two eqilibria for some parameters. The existence of heteroclinic orbits of Shil'nikov type in a chaotic system has been proved by using the undetermined coefficient method. As a result, the Shil'nikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of attractor are determined by these heteroclinic orbits.

Received: May 14, 2006

AMS Subject Classification: 37G10 37D45 37G35

Key Words and Phrases: chaos, heteroclinic orbits, Shil'nikov criterion

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3