Bifurcation of limit cycles from a heteroclinic loop with a cusp
Copyright policy )Bifurcation of limit cycles from a heteroclinic loop with a cusp
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.
- Shanghai Normal University China (People's Republic of)
- Hebei Normal University China (People's Republic of)
Bifurcation theory for ordinary differential equations, limit cycle, Melnikov function, heteroclinic loop, bifurcation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Homoclinic and heteroclinic solutions to ordinary differential equations, nilpotent cusp
Bifurcation theory for ordinary differential equations, limit cycle, Melnikov function, heteroclinic loop, bifurcation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Homoclinic and heteroclinic solutions to ordinary differential equations, nilpotent cusp
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