Dynamic characteristics of a simple bursting neuron model

We present a simple neuron model that shows a rich property in spite of the simple structure derived from the simplification of the Hindmarsh-Rose, the Morris-Lecar, and the Hodgkin-Huxley models. 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 is explained in connection with the disposition of the active areas on the potential, and hence we are able to discuss the global dynamic behaviors and the common properties among these realistic models. The obtained outputs are broadly classified as simple oscillations, spiking, bursting, and chaotic oscillations. The bursting outputs are classified as with spike undershoot and without spike undershoot, and the bursts without spike undershoot are classified as with tapered and without tapered. We show the parameter dependence of these outputs and discuss the connection between these outputs and the potential with active areas.