Fig. 2.

Bifurcation diagram of the full system. (A) Codimension-two bifurcation diagram as a function of $\alpha$ and $\beta$. Orange regions indicate the presence of stable oscillations, and yellow regions indicate the presence of unstable oscillations. Parameters are the same as in Table 1. Blue lines, homoclinic bifurcations; dashed black lines, subcritical Hopf bifurcation; GH, generalized Hopf bifurcation (Bautin); green lines, saddle node; purple lines, transcritical; solid black lines, supercritical Hopf bifurcation. (B) Codimension-one slices of the above bifurcations for fixed $\beta =0.4$ (B1) or $\alpha =0.4$ (B2). Blue solid (dashed) lines correspond to stable (unstable) fixed points, solid (dashed) pink lines correspond to the maximum and minimum G values on a stable (unstable) cycle, and circles correspond to heteroclinic orbits (blue stars depict the fixed points belonging to the orbit). Bifurcations indicated on the graph split the diagram into four regions (woodland, oscillations, bistability, and forest; B1) or grassland, woodland, and oscillations (B2). C1 (β = 0.2) and C2 (parameters as in B2) represent a selection of typical dynamics in the regions depicted in B1 and B2.