Hopf bifurcations in normal forms of third order nonlinear affine control systems

The paper investigates Hopf bifurcations in a class of simple nonlinear systems, i.e., third order affine control systems described in terms of “quadratic plus cubic” normal forms and subject to linear state feedback control laws. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical bifurcations is analytically determined. Also, a second order harmonic approximation of the bifurcated periodic solution is provided. Such analytical results can be exploited as starting points to investigate complex behaviours of the considered class of simple nonlinear systems.