CUED Publications database

The geometry of rest–spike bistability

Cirillo, GI and Sepulchre, R (2020) The geometry of rest–spike bistability. Journal of Mathematical Neuroscience, 10.

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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.

Item Type: Article
Uncontrolled Keywords: math.DS math.DS q-bio.NC 92B25, 92C20, 34C26, 34C60
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 12 May 2019 20:04
Last Modified: 15 Apr 2021 06:35
DOI: 10.1186/s13408-020-00090-z