Bistable Dynamics Underlying Excitability of Ion Homeostasis in Neuron Models
Figure 2
Bifurcation diagram of the ion–based model.
Bifurcations are marked by red circles, the physiological equilibrium by a green square. Following the z–shaped fixed point characteristic from below there are two saddle–node bifurcations (limit point, LP) at
and
, and three subcritical Hopf bifurcations (HB) at
,
and
. The limit cycles created in HB1, HB2 and HB3 disappear in homoclinic bifurcations (HOM) at
,
and
, respectively. The second LP and the second HB together with the HOM of limit cycles occur in a very narrow parameter range (see blow–up inset). The number of stable (
) and unstable (
) directions of the fixed point is indicated by the
–tuples. There is bistability of a physiological state and a depolarized state with largely reduced ion concentration gradients between
and
.