Complex behaviour analysis in quadratic jerk systems via frequency domain Hopf bifurcation

The paper deals with the characterization of Hopf bifurcations in families of third order autonomous systems involving quadratic nonlinearities. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical bifurcations is analytically determined, together with an approximation of the actual bifurcated periodic solution. It is believed that these analytical results can be exploited in order to locate via bifurcation analysis simple systems able to display complex behaviors.