A Simple Neuron Model


The full dynamics of a neuron can be quite complicated and depend on many fine tuned parameters. Izhikevich provides a simplified model for neurons in chapter 10 from his book Dynamical Systems in Neuroscience. This simplified model while not physiologically accurate provides the same geometric properties observed in real neurons. The model has two dynamical variables, the normalized membrane voltage and a recovery variable, that obey the following relations. </p>

$$\dot{v}=I+v^2-u \\ \dot{u}=a(bv-u) \\ if\, v>1 \\ v\leftarrow c, \, u\leftarrow u+d $$

Below you can manipulate the quiescent parameters and see what effect it has on the neurons action. Further there are some predetermined parameters that exhibit certain behaviors of neurons, such as constant spiking, firing in bursts and sub threshold oscillations. a determines the time constant of the recovery parameter. b determines whether the neuron is an integrator or an oscilator. c is the depolarization after potential and models the slow activation of the recovery parameter during bursting.