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The geometry of rest-spike bistability.

Published version
Peer-reviewed

Type

Article

Change log

Authors

Cirillo, Giuseppe Ilario  ORCID logo  https://orcid.org/0000-0002-1162-3225
Sepulchre, Rodolphe 

Abstract

Morris-Lecar model is arguably the simplest dynamical model that retains both the slow-fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamical system is a core structure for many dynamical phenomena such as slow spiking and bursting. We show how the proposed model combines physiological interpretation and mathematical tractability and we discuss the benefits of the proposed approach with respect to alternative models in the literature.

Description

Keywords

Neuronal models, Rest–spike bistability, Slow–fast models

Journal Title

J Math Neurosci

Conference Name

Journal ISSN

2190-8567
2190-8567

Volume Title

10

Publisher

Springer Science and Business Media LLC
Sponsorship
European Research Council (670645)