Special cubic perturbations of the Duffing oscillator $x"=x-x^3$ 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 $x"=x-x^3$ under the special cubic perturbation $$ x"= x-x^{3}+λ_{1}…