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arXiv · 2003.12280

Zero-Hopf bifurcation in a 3-D jerk system

Francisco Braun·Ana C. Mereu
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Abstract

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

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Francisco Braun, Ana C. Mereu. 2020-03-27. Zero-Hopf bifurcation in a 3-D jerk system. https://doi.org/10.1016/j.nonrwa.2020.103245

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