Showing math.DSShow all
3 papers · 1 filter
math.DS2019
Special cubic perturbations of the Duffing oscillator near the eight-loop
Lubomir Gavrilov, Ameni Gargouri, Bassem Ben Hamed
We find an upper bound for the number of limit cycles, bifurcating from the 8-loop of the Duffing oscillator under the special cubic perturbation $$ x"= x-x^{3}+λ_{1}…
math.DS2016
Cubic Perturbations of Symmetric elliptic Hamiltonians of degree four in a Complex domain
Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov
We consider arbitrary one-parameter cubic deformations of the Duffing oscillator . In the case when the first Melnikov function vanishes, but we compute…
math.DS2014
Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov
The cyclicity of the exterior period annulus of the asymmetrically perturbed Duffing oscillator is a well known problem extensively studied in the literature. In the present paper…