Homoclinic loop and multiple limit cycle bifurcation surfaces

Perko, L. M.

doi:10.1090/S0002-9947-1994-1227092-6

Homoclinic loop and multiple limit cycle bifurcation surfaces
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Trans. Amer. Math. Soc. 344 (1994), 101-130 Request permission

Abstract:

This paper establishes the existence and analyticity of homoclinic loop bifurcation surfaces $\mathcal {H}$ and multiplicity-two, limit cycle bifurcation surfaces $\mathcal {C}$ for planar systems depending on two or more parameters; it determines the side of $\mathcal {H}$ or $\mathcal {C}$ on which limit cycles occur; and it shows that if $\mathcal {H}$ and $\mathcal {C}$ intersect, then typically they do so at a flat contact.

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