Order Reduction for Dynamical Systems Describing the Behavior of Complex Neurons

We have devised a scheme to reduce the complexity of dynamical systems belonging to a class that includes most biophysically realistic neural models. The reduction is based on transformations of variables and perturbation expansions and it preserves a high level of fidelity to the original system. The techniques are illustrated by reductions of the Hodgkin-Huxley system and an augmented Hodgkin-Huxley system.