# LIF cells¶

The description of a LIF cell is used to control the leaky integrate-and-fire dynamics:

• Starting potential $$V_\mathrm{0}$$, by default $$V_\mathrm{0} = E_\mathrm{L}$$

• Resting potential $$E_\mathrm{L}$$

• Reset potential $$E_\mathrm{R}$$, by default $$E_\mathrm{R} = E_\mathrm{L}$$

• Membrane potential decaying constant $$\tau_\mathrm{m}$$

• Membrane capacitance $$C_\mathrm{m}$$

• Firing threshold $$U_\mathrm{threshold}$$

• Refractory period $$t_\mathrm{ref}$$

The morphology of a LIF cell is automatically modelled as a single compartment; each cell has one built-in source and one built-in target which need to be given labels when the cell is created. The labels are used to form connections to and from the cell. LIF cells do not support adding additional sources or targets to the description. They do not support gap junctions. They do not support adding density or point mechanisms.

The LIF cell’s time dynamics are this:

1. $$U_\mathrm{m}(0) = V_\mathrm{0}$$,

2. If the cell is in its refractory state $$U_\mathrm{m}(t) = E_\mathrm{R}$$

3. Otherwise $$U'_\mathrm{m}(t) = \sum\limits_\mathrm{spike} w_\mathrm{spike}\cdot\delta(t - t_\mathrm{spike}) - \frac{1}{\tau_\mathrm{m}}\left(U_\mathrm{m}(t)) - E_\mathrm{L}\right)$$ where $$w_\mathrm{spike}$$ represents the weight of the synaptic connection associated with the given spike event.

4. If $$U_\mathrm{m}(t_0) \geq U_\mathrm{threshold}$$: emit spike and enter refractory period until $$t = t_0 + t_\mathrm{ref}$$

LIF cells can be probed to obtain their current membrane potential, see Probing and Sampling.