Abstract
The purpose of this paper is to propose some coefficient conditions,
characterizing the stability of periodic solutions bifurcated from
zero-Hopf bifurcations of the general quadratic jerk system, and apply
these theoretical results to a special jerk system in order to predict
chaos. First, we characterize the zero-Hopf bifurcations of the general
quadratic jerk system in $\mathbb{R}^3$. The
coefficient conditions on stability of periodic solutions are obtained
via the averaging theory of first order. Next, we apply the theoretical
results to a two-parameter jerk system. Finally special attention is
paid to a jerk system with one non-negative parameter
$\epsilon$ and one non-linearity. By studying the
continuation of periodic solution initiating at the zero-Hopf
bifurcation, we numerically find a sequence of period doubling
bifurcations which leads to the creation of chaotic attractor.