## 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.