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May 2012, 17(3): 915-932. doi: 10.3934/dcdsb.2012.17.915
On the stability of homoclinic loops with higher dimension
Xingbo Liu 1, and Deming Zhu 1,
Department of Mathematics, East China Normal University, Shanghai, 200241
Received September 2010 Revised March 2011 Published January 2012
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.
Keywords: homoclinic orbits, moving frame., Stability.
Mathematics Subject Classification: Primary: 34C23, 34C37; Secondary: 37C2.
Citation: Xingbo Liu, Deming Zhu. On the stability of homoclinic loops with higher dimension. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 915-932. doi: 10.3934/dcdsb.2012.17.915
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Xingbo Liu Deming Zhu