Figure 4

Bifurcation diagrams of (2a)–(2h) with as a function of \((B, C_{3})\). (a) Bifurcation diagram of (2a)–(2h) on the \((B, C_{3})\) plane. Curves are named, respectively, after the limit point (LP, black curves), Hopf (H, red curves) and homoclinic (HOM, blue curves) bifurcations in panels (b–f). Only the LP bifurcations interacting with canard solutions are plotted. Black squares indicate cusp (CP), red circles indicate Bogdanov–Takens (BT) and red squares indicate generalized Hopf (GF) bifurcations. The regions marked by black, green and purple boxes are zoomed in black, green and purple framed insets. The region where the homoclinic curve tips to the \(LP_{1}\) is zoomed inside the green inset. (b–f) Bifurcation diagrams of (2a)–(2h) as a function of B for different values of \(C_{3}\). The limit point bifurcations of interest are marked by black squares, Hopf bifurcations by red circles, and homoclinic connections by blue stars. Stable and unstable solutions are represented by continuous and dashed curves, respectively. Along the curves of equilibrium points, (2a)–(2h) undergoes four Hopf bifurcations (\(H_{1,2,3,4}\)) for \(C_{3}=\{50,80,145\}\) (c, d, e) and three Hopf bifurcations (\(H_{1,2,3}\)) for \(C_{3}=15\) (b) and (\(H_{1,2,4}\)) for \(C_{3}=200\) (f)