  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.
