Three- and two-dimensional bifurcation diagrams in the weak-inhibition regime.

<p>Left, <i>μ</i>_<i>E</i> is shown on the <i>z</i>−axis as function of <i>I</i>_<i>E</i>−<i>I</i>_<i>I</i>. Here we plot only the local bifurcations (blue: saddle-node curves, red: Andronov-Hopf curves) that bound the plain/dashed regions representing the stable/unstable equilibrium point areas. Right, complete set of codimension two bifurcations. The Andronov-Hopf bifurcation curves (red lines) are divided into supercritical (plain) and subcritical (dashed) portions. The supercritical/subcritical portions are bounded by a generalized Hopf bifurcation, GH, and Bogdanov-Takens bifurcations, BT. The latter are the contact points among saddle-node bifurcation curves (blue lines), Andronov-Hopf bifurcation curves (red lines), and homoclinic bifurcation curves (hyperbolic-saddle/saddle-node homoclinic bifurcations are described by plain/dashed orange curves). SNIC bifurcations identify the contact point between the saddle-node curve and the homoclinic one. From GH originate two limit point of cycles curves (dark green lines) that collapse into the homoclinic curves. Before this, they present a cusp bifurcation, CPC. Each saddle-node curve shows, in addition to BT, a cusp bifurcation, CP.