On the stability of homoclinic loops with higher dimension

Xingbo Liu; Deming Zhu

doi:10.3934/dcdsb.2012.17.915

Article Contents

2012, Volume 17, Issue 3: 915-932. Doi: 10.3934/dcdsb.2012.17.915

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On the stability of homoclinic loops with higher dimension

Xingbo Liu^1, and
Deming Zhu^1,

1.
Department of Mathematics, East China Normal University, Shanghai, 200241

Received: August 31, 2010

Revised: February 28, 2011

Published: April 2012

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Abstract

In this paper the stability of homoclinic loops of saddle equilibrium states in high dimensional systems is analyzed. By constructing local moving frame along the unperturbed homoclinic orbit, the refined Poincaré map is well established, and simple criteria are given for the stability of the saddle homoclinic loop. Some known results are extended.

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Mathematics Subject Classification: Primary: 34C23, 34C37; Secondary: 37C29.

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