Bifurcation of limit cycles from a heteroclinic loop with a cusp (Q531690)
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scientific article; zbMATH DE number 5880253
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcation of limit cycles from a heteroclinic loop with a cusp |
scientific article; zbMATH DE number 5880253 |
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Bifurcation of limit cycles from a heteroclinic loop with a cusp (English)
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19 April 2011
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Bifurcation of limit cycles is studied by investigating the expansion of the first Melnikov function of a near-Hamiltonian system \[ x' = H_y +\varepsilon p(x, y, \delta),\quad y' = -H_x +\varepsilon q(x, y, \delta) \] near a heteroclinic loop with a cusp and a saddle or two cusps. Using the formulae obtained for computing the first coefficients of the expansion, results on bifurcation are obtained for some polynomial systems. This is a continuation of the authors' previous publications in this area.
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nilpotent cusp
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heteroclinic loop
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limit cycle
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bifurcation
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Melnikov function
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