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.
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Contributed by Li Ji-bin
Project supported by the Key Project of the National Natural Science Foundation of China (Nos. 40233029 and 40221503)
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Hai-ying, L., Ji-bin, L. What are the separatrix values named by Leontovich on homoclinic bifurcation. Appl Math Mech 26, 457–464 (2005). https://doi.org/10.1007/BF02465384
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DOI: https://doi.org/10.1007/BF02465384