## Classification

# of variables | # of modes | # of jumps |
---|---|---|

2 | 1 | 1 |

Type | Continuous dynamics | Guards & Invariants | Resets |
---|---|---|---|

hybrid | linear polynomial | linear polynomial | linear polynomial |

## Download

Flow* model I | neuron_I.model |

Flow* model II | neuron_II.model |

## Description of model I

The general dynamics of the model of spiking neurons is defined by the following ODE.

wherein the constant parameters are given by , , , , and . The value of is when , otherwise it is . Whenever the value of reaches , its value is reset to and meanwhile is updated to .

## Reachability settings for model I

We consider the initial set defined by , .

## Results for model I

The following figures show an overapproximation computed by Flow* for the time horizon .

## Description of model II

As the second example, the constant parameters are given by , , , , , and . The values of , are reset to and respectively when .

## Reachability settings for model II

We consider the initial set defined by , .

## Results for model II

The following figures show an overapproximation computed by Flow* for the time horizon .

## References

[1] E. Izhikevich.*Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting.*The MIT Press, 2010.