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Mathematics > Dynamical Systems
Title: The geometry of rest-spike bistability
(Submitted on 27 Apr 2019 (v1), last revised 2 Sep 2020 (this version, v4))
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.
Submission history
From: Giuseppe Ilario Cirillo [view email][v1] Sat, 27 Apr 2019 14:29:07 GMT (348kb,D)
[v2] Wed, 29 Jan 2020 16:49:15 GMT (331kb,D)
[v3] Thu, 23 Jul 2020 16:06:05 GMT (331kb,D)
[v4] Wed, 2 Sep 2020 15:23:57 GMT (331kb,D)
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