Green line corresponds to a saddle-node bifurcation of limit cycles.
Thus it is more likely to observe a (large) saddle homoclinic in one parameter continuation of neural models, although it might be very close to a saddle-node and, hence, be mistaken for a SNIC.
The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis.
The problems at the end of the chapter allow students to explore a saddle-node bifurcation in a one-dimensional system.
However, for g SI ≈ 0.7672 mS/cm 2, that is, just before the transition from five to six spikes, a saddle-node bifurcation occurs on the saddle-unstable sheet S 1 r.
For SNIC bifurcations to appear with a saddle-node near the fold point (F^), we will hence impose the following condition.
For example, small changes in a parameter value can cause a pair of attractor and saddle points to appear or disappear through a saddle-node or fold bifurcation, or an attractor can be turned into a saddle point through a transcritical bifurcation.
The a parameter was fixed to −5, 0.001 or 30 nS, corresponding to a system loosing stability via a saddle-node (Fig. 6a– d) or Andronov-Hopf (Fig. 6e, f) bifurcation.
Crossing a saddle-node bifurcation to areas 2 or 5, two equilibria with high excitatory activity appear.
As in the case of the saddle homoclinics, denote by (x_{S}^) the intersection of the section S with the unstable separatrix of the singularity (p_), up to the point where it becomes a saddle-node.
