# Izhikevich Neuron

The Izhikevich model neuron was developed as an efficient, powerful alternative to the integrate and fire model. The model uses two variables, a variable representing voltage potential and another representing membrane recovery (activation of potassium currents and inactivation of sodium currents).

To explore this neuron, you can use the script *spikingNeuronDemo.bsh*, from the workspace script menu.

This is a spiking neuron, so when the voltage passes a threshold value a spiking event occurs, the GUI neuron turns yellow, and the voltage and recovery variable are reset.

Since *a* is a parameter of the model, we use *v* to represent activation (voltage potential). *u* represents the recovery variable. Voltage is computed by integrating the following two differential equations using Euler's method:

*W* is weighted inputs; *a *and *b *are abstract parameters of the model.

When the voltage exceeds a threshold value, which is preset at 30, both *v* and *u* are reset, as follows:

Thus there are four parameters for this system. According to Izhikivech, "The model can exhibit firing patterns of all known types of cortical neurons with [a suitable] choice of parameters"

Links / References

Izhikevich's page discussing this model.

Eugene Izhikevich (2004), "Which Model to Use For Cortical Spiking Neurons," *IEEE Transactions on Neural Networks.*

Parameters

Time step

See time-step (Izhikevich uses .2 in his paper.)

A

Parameter for recovery variable.

B

Parameter for recovery variable.

C

The value for

vwhich occurs after a spike.

D

A constant value added to

uafter spikes.

Ibg

Constant background current.

Add Noise

If this is set to true, random values are added to the activation via a noise generator. For details of how the noise generator works, click here.

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 |