Figure 8

Bifurcation diagram for \(\bar{\mathcal{S}}^{-}_{ \mathrm{osc}}\) in the case \(\beta _{\epsilon 0R} > 0\), \(C_{ \mathrm{det}} + \beta _{\epsilon 0R} > 0\) and \(\beta _{\epsilon 0R} < - C_{\mathrm{det}} + \sqrt{C^{2}_{\mathrm{det}} + \beta ^{2}_{\epsilon 0I}}\). The fixed point \(\bar{\mathcal{S}}^{-}_{\mathrm{osc}}\) appears at a supercritical pitchfork bifurcation of the origin occurring at the curve \(C^{-}_{\mathrm{HB}}\), undergoes a Hopf bifurcation \(\bar{ \mathcal{H}}\) at the curve \(\operatorname{Tr}^{-}=0\) and becomes unstable at the curve \(\operatorname{Det}^{-}=0\)