Fig. 8

Sketch of bifurcation diagram in \((a,c)\) parameter space for \(0<\varepsilon \ll1\): cusp bifurcation and SN branches (black); Bautin bifurcation point (red) with Andronov–Hopf branches (sub = dashed/super = solid); and saddle-node of periodic orbit (SNPO) branch (green); small and large homoclinic (\(\mathit{HOM}_{s}\) and \(\mathit{HOM}_{\ell}\)) branches (blue); SNIC segment (blue) on the SN branch \(a_{\mathrm{sn}}^{-}\)