A critical extension to the Leaky Integrate and Fire model is the addition of a dynamic threshold. In this model, the threshold changes with time, introducing critical properties such as spike frequency adaptation, relative refractoriness, and negative interspike interval correlations.
In the future, I hope to do a more thorough review of threshold models, but our first paper (2015) does a pretty decent job.
I’ve put together an implementation of a standard LIF model with dynamic threshold, following the work of Chacron, Longtin, and Maler in their 2001 paper “Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli.” Not all the features of their model have been implemented in my code, but the critical dynamic threshold is there.
The model is here: https://bitbucket.org/erikjohnson24/eriksresearchcode/src/master/neural/lif_dt.m
And testing code: https://bitbucket.org/erikjohnson24/eriksresearchcode/src/master/neural/test_lif_dt.m