Relationship between threshold and bifurcations for paradoxical firing responses along with seizure induced by inhibitory stimulation

Abstract

Inhibition-induced enhancement or paradoxical response of firing was related to Hopf bifurcation instead of saddle-node bifurcation on an invariant cycle (SNIC), due to the ``negative" threshold and rotated vector fields. In the present Letter, by changing multiple parameters to adjust the vector fields, condition for the paradoxical response and ``negative" threshold is extended to SNIC near a codimension-2 bifurcation appearing prior to the Hopf bifurcation, which presents a comprehensive relationship between bifurcations and threshold. Especially, the result for a special current can well explain the enhanced firing along with seizure induced by inhibitory interneuron, implying that SNIC far from the codimension-2 bifurcation of pyramidal neuron is a potential candidate to avoid seizure.