Shape of the basin of limit cycle of Hodgkin-Huxley model in 4 dimensional initial value space

The structure of the basin of limit cycle of Hodgkin-Huxley model was investigated by carrying out the numerical simulations. As the Hodgkin-Huxley model has four variables, the basin of limit cycle of Hodgkin-Huxley model has 4-D structure. The external input current to the Hodgkin-Huxley neuron was important factor for repeated firing, i.e., the limit cycle solution. When the external input current is low, there is no stable limit cycle solution. In general, the area of basin of limit cycle increases with external input current. We determined the detailed shape of the basin in 4 dimensional space by changing the external input to Hodgkin-Huxley neuron