What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation
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摘要: 由Leontovich定义的鞍点量和分界线量是判断同宿轨道分支出极限环的数目及同宿环稳定性的主要判据.利用Tkachev对多重极限环稳定性判定的方法,对给定的系统,得到了同宿环分支的第三阶分界线量的公式,并对高阶分界线量做了猜测.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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Key words:
- homoclinic bifurcation /
- separatrix value /
- saddle value /
- limit cycle
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