The Stability and Chaotic Motions of a Four-Wing Chaotic Attractor

Xia Wang; Jian Ping Li; Jian Yin Fang

doi:10.4028/www.scientific.net/AMM.48-49.1315

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 48-49The Stability and Chaotic Motions of a Four-Wing...

The Stability and Chaotic Motions of a Four-Wing Chaotic Attractor

Abstract:

The stability and chaotic motions of a 3-D quadratic autonomous system with a four-wing chaotic attractor are investigated in this paper. Base on the linearization analysis, the stability of the equilibrium points is studied. By using the undetermined coefficient method, the heteroclinic orbits are found and the convergence of the series expansions of this type of orbits is proved. It analytically demonstrates that there exist heteroclinic orbits of Silnikov type connecting the equilibrium points. Therefore, Smale horseshoes and the horseshoe chaos occur for this system via the Silnikov criterion.

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Periodical:

Applied Mechanics and Materials (Volumes 48-49)

Pages:

1315-1318

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.48-49.1315

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Online since:

February 2011

Authors:

Xia Wang, Jian Ping Li, Jian Yin Fang

Keywords:

Chaos, Heteroclinic Orbits, Smale Horseshoes, Undetermined Coefficient Method

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