Bursting characteristics of a neuron model based on a concept of potential with active areas.

We present various bursting wave forms that are obtained from a simple model of the Hodgkin-Huxley type. The model is a typical example whose characteristics can be discussed through the concept of potential with active areas. A potential function is able to provide a global landscape for dynamics of a model, and the dynamics are explained in relation to the disposition of the active areas on the potential. We obtain the potential functions and the active areas for the Hindmarsh-Rose model, the Morris-Lecar system, and the Hodgkin-Huxley system, and hence, we are able to discuss the common properties among these models based on the concept of potential with active areas.