Fig. 11

The left panel shows bifurcations of Eq. (7) in the spatially homogeneous case, organized around the Bogdanov–Takens (BT) bifurcation. SN1 and SN2 are saddle-node bifurcations. AH is an Andronov–Hopf bifurcation, and SHO is a saddle homoclinic-orbit bifurcation. Note that a and b are the control parameters introduced earlier. The right panel shows the nullcline structure of a Bogdanov–Takens bifurcation. At the Bogdanov–Takens point, a stable node (open circle) coalesces with an unstable point. [Redrawn from [34]]