Zero-Hopf bifurcation in a 3D jerk system

We consider the 3-D system defined by jerk equation $\dddot{x} = -a \ddot{x} + x \dot{x}^2 -x^3 -b c \dot{x}$, with $a, b, c\in \mathbb{R}$. When $a=b=0$ and $c < 0$ equilibrium point localized at origin is a zero-Hopf equilibrium. analyse Bifurcation that occur this when we persuade quadratic perturbation of coefficients, prove one, two or three periodic orbits can born parameter goes to $0$.