What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation

LUO Hai-ying; LI Ji-bin

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LUO Hai-ying, LI Ji-bin. What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation[J]. Applied Mathematics and Mechanics, 2005, 26(4): 418-425.

Citation:

LUO Hai-ying, LI Ji-bin. What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation[J]. Applied Mathematics and Mechanics, 2005, 26(4): 418-425.

Citation:

LUO Hai-ying, LI Ji-bin. What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation[J]. Applied Mathematics and Mechanics, 2005, 26(4): 418-425.

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What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation

LUO Hai-ying^1,2,3,,
LI Ji-bin²

1.
LASG, Institute of Atmospheric Physics, Chinese Academy of Science, Beijing 100029, P. R. China;

Received Date: 2003-06-20
Rev Recd Date: 2004-12-03
Publish Date: 2005-04-15

Abstract

Abstract

For a given system,by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle,the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given,which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop,and a computation formula for higher separatrix values was conjectured.
- homoclinic bifurcation,
- separatrix value,
- saddle value,
- limit cycle

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References(18)

References

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