# On dependency properties of the ISIs generated by a two-compartmental neuronal model

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## Abstract

One-dimensional leaky integrate and fire neuronal models describe interspike intervals (ISIs) of a neuron as a renewal process and disregarding the neuron geometry. Many multi-compartment models account for the geometrical features of the neuron but are too complex for their mathematical tractability. Leaky integrate and fire two-compartment models seem a good compromise between mathematical tractability and an improved realism. They indeed allow to relax the renewal hypothesis, typical of one-dimensional models, without introducing too strong mathematical difficulties. Here, we pursue the analysis of the two-compartment model studied by Lansky and Rodriguez (Phys D 132:267–286, 1999), aiming of introducing some specific mathematical results used together with simulation techniques. With the aid of these methods, we investigate dependency properties of ISIs for different values of the model parameters. We show that an increase of the input increases the strength of the dependence between successive ISIs.

## Keywords

Two-compartment neural model ISI dependency properties## Notes

### Acknowledgments

This work was supported in part by MIUR Project PRIN-Cofin 2008. The authors are grateful to Petr Lansky for useful suggestions and to the anonymous referees for their constructive comments.

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