Theta-Neuron Model

Definition

Theta-neuron is a one-dimensional neural model that describes the state of the neuron with a phase variable:

$$ {\theta}^{\prime }=\left(1- \cos \theta \right)+\left(1+ \cos \theta \right)\left(\beta +\mathrm{Inputs}(t)\right) $$

(1)

where θ is between 0 and 2π, β is a constant parameter, and Inputs(t) summarize the time-dependent inputs to the model.

Theta-neuron is equivalent to the quadratic integrate-and-fire (QIF) neuron or the quadratic normal form for the SNIC bifurcation, making the theta-neuron a canonical neural model: in a sense all models exhibiting the SNIC bifurcation can be reduced (in a sufficiently local neighborhood of the bifurcation) to the theta-neuron.

Detailed Description

The theta-neuron, also known as the Ermentrout-Kopell canonical model, was first derived in Ermentrout and Kopell (1986) to study bursting activity in coupled networks. While the initial intent of this model was to model neuronal oscillators, subsequent works used the theta-neuron as...