Using Melnikov functions of any order for studying limit cycles
Copyright policy )Using Melnikov functions of any order for studying limit cycles
The planar system investigated in the paper is related to Hilbert's 16th problem. The author studies a class of quadratic Hamiltonian systems perturbed with general quadratic polynomials in order to identify the maximum number of limit cycles. He derived the Melnikov functions arisen from the displacement function of the first return map. By choosing appropriate system parametric values and taking into account the Melnikov functions of any order, the author shows that the planar system has at most three limit cycles which bifurcate from the period annulus of the unperturbed system and this upper bound is reached.
Bifurcation theory for ordinary differential equations, Perturbations, asymptotics of solutions to ordinary differential equations, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Hamiltonian systems, Melnikov functions
Bifurcation theory for ordinary differential equations, Perturbations, asymptotics of solutions to ordinary differential equations, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Hamiltonian systems, Melnikov functions
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