Complex oscillations and chaos in a simple neuron model

To study the factors that contribute to the changes of burst patterns, the author formulates a four-variable neuronal model. The model contains (i) a voltage-dependent fast Na⁺ current that is responsible for the upstroke of spikes; (ii) a delayed rectifying voltage-gated K⁺ current which is responsible for the repolarization of spikes; (iii) a voltage-activated slow Ca²⁺ current which brings about a slow underlying wave; and (iv) the intracellular Ca²⁺ concentration which inactivates the Ca²⁺ current. With this model, the author shows how the model neuron can transform simple oscillations to bursting, to chaos, and to multi-peaked oscillations, as the opening of the gates of K⁺ and Ca²⁺ channels slows down. The present simulation thus indicates that the channel gating variables are very important in the generation of chaotic signaling