Hindmarsh–Rose model

The relevant variable is the membrane potential, x(t), which is written in dimensionless units.

z(t) corresponds to an adaptation current, which is incremented at every spike, leading to a decrease in the firing rate.

Then, the Hindmarsh–Rose model has the mathematical form of a system of three nonlinear ordinary differential equations on the dimensionless dynamical variables x(t), y(t), and z(t).

The parameter r governs the time scale of the neural adaptation and is something of the order of 10−3, and I ranges between −10 and 10.

This makes the Hindmarsh–Rose model relatively simple and provides a good qualitative description of the many different patterns that are observed empirically.