Izhikevich Neuron
The Izhikevich model neuron was developed as an efficient, powerful alternative to the integrate and fire model. This is a spiking neuron, so when the voltage passes a threshold value a spiking event occurs, and the neuron and outgoing connection turns yellow.
The model uses two variables, a variable representing voltage potential \(v\) and another variable \(u\) representing membrane recovery (activation of potassium currents and inactivation of sodium currents). The voltage potential \(v\) corresponds to the “activation” of the neuron that determines what color it is represented as.
The variables \(u\) and \(v\) are governed by these differential equations:
\[\begin{align*} \dot{v} &= .04 v^2 + 5v + 140 - u + I \\[2mm] \dot{u} &= a(bv - u) \\ \end{align*}\]Where \(I\) is the total input (net input from other neurons plus background current). The other parameters are described below. Whenever \(v \geq v_{peak}\) a spike occurs and the voltage and recovery variable are reset:
\[\begin{align*} v &\leftarrow c \\[2mm] u &\leftarrow u + d \\ \end{align*}\]To explore this model, you can use the script spikingNeuronDemo.bsh, from the workspace script menu.
This version of them model is from Eugene Izhikevich (2004), “Which Model to Use For Cortical Spiking Neurons,” IEEE Transactions on Neural Networks. He updates the model slightly in his book. Dynamical Systems in Neuroscience. Also see his webpage about the model.
Parameters
- A: Controls the time scale of the recovery variable. Smaller values make recovery slower.
- B: Sensitivity of the recovery variable to voltage.
- C: Membrane potential reset value after a spike.
- D: Recovery variable increment after a spike.
- Threshold: Value of \(v\) that triggers a spike and reset.
- I bkgd: Constant background current applied each time step.
For all other parameters, see common neuron properties
Some useful Parameter Settings
(See link above for more information)
| A | B | C | D | I (Input) | |
|---|---|---|---|---|---|
| Tonic spiking | 0.02 | 0.2 | -65 | 6 | 14 |
| Phasic spiking | 0.02 | 0.25 | -65 | 6 | 0.5 |
| Tonic bursting | 0.02 | 0.2 | -50 | 2 | 15 |
| Phasic bursting | 0.02 | 0.25 | -55 | 0.05 | 0.6 |
| Mixed mode | 0.02 | 0.2 | -55 | 4 | 10 |
| Spike frequency adaptation | 0.01 | 0.2 | -65 | 8 | 30 |
| Class 1 | 0.02 | -0.1 | -55 | 6 | 0 |
| Class 2 | 0.2 | 0.26 | -65 | 0 | 0 |
| Spike latency | 0.02 | 0.2 | -65 | 6 | 7 |
| Subthreshold oscillations | 0.05 | 0.26 | -60 | 0 | 0 |
| Resonator | 0.1 | 0.26 | -60 | -1 | 0 |
| Integrator | 0.02 | -0.1 | -55 | 6 | 0 |
| Rebound spike | 0.03 | 0.25 | -60 | 4 | 0 |
| Rebound burst | 0.03 | 0.25 | -52 | 0 | 0 |
| Threshold variability | 0.03 | 0.25 | -60 | 4 | 0 |
| Bistability | 1 | 1.5 | -60 | 0 | -65 |
| DAP | 1 | 0.2 | -60 | -21 | 0 |
| Accomodation | 0.02 | 1 | -55 | 4 | 0 |
| Inhibition-induced spiking | -0.02 | -1 | -60 | 8 | 80 |
| Inhibition-induced bursting | -0.026 | -1 | -45 | 0 | 80 |