Ions conductance and external-stimulation dependent bifurcations.

By analyzing the Hodgkin-Huxley model, it can be estimated how neurons communicate with each other. It is the most widely used model that describes why the action potentials happen and how action potentials are generated and propagated in neurons. In a nerve cell, an action potential is evoked when the membrane potential attains its threshold (bifurcation point of neuron activity) membrane potential. The substantive changes associated with membrane voltage and conductance driving the action potential. Sometimes, nerve cells show abnormal activity for different causes. In this paper, we analyze the bifurcation of the Hodgkin-Huxley model to show the relationship between the abnormal activity of the nerve cells and the ionic conductance and external stimulation into the nerve cells. We also illustrated the possible region where the nerve cells show undesirable hyperactivity by calculating the Hopf bifurcation curve. [ABSTRACT FROM AUTHOR]