title: Unfolding an electronic integrate-and-fire circuit.
abstract: Many physical and biological phenomena involve accumulation and discharge processes that can occur on significantly different time scales. Models of these processes have contributed to understand excitability self-sustained oscillations and synchronization in arrays of oscillators. Integrate-and-fire (I+F) models are popular minimal fill-and-flush mathematical models. They are used in neuroscience to study spiking and phase locking in single neuron membranes, large scale neural networks, and in a variety of applications in physics and electrical engineering. We show here how the classical first-order I+F model fits into the theory of nonlinear oscillators of van der Pol type by demonstrating that a particular second-order oscillator having small parameters converges in a singular perturbation limit to the I+F model. In this sense, our study provides a novel unfolding of such models and it identifies a constructible electronic circuit that is closely related to I+F.
authors.affiliation: Laboratorio de Dinámica no Lineal, Facultad de Ciencias y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico, DF, Mexico.
authors.forename: Humberto
authors.initials: H
authors.lastname: Carrillo
authors.forename: Frank
authors.initials: F
authors.lastname: Hoppensteadt
mesh_terms: D001683:Biological Clocks / Q000502:physiology; D004581:Electronics; D008433:Mathematics; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*