A two-state neuronal model with alternating exponential excitation

We develop a stochastic neural model based on point excitatory inputs. The nerve cell depolarisation is determined by a two-state point process corresponding the two states of the cell. The model presumes state-dependent excitatory stimuli amplitudes and decay rates of membrane potential. The state switches at each stimulus time. We analyse the neural firing time distribution and the mean firing time. The limit of the firing time at a definitive scaling condition is also obtained. The results are based on an analysis of the first crossing time of the depolarisation process through the firing threshold. The Laplace transform technique is widely used. © 2019 the author.

• Fecha de publicación: 2019
• Institución: Universidad del Rosario
• Repositorio: Repositorio EdocUR - U. Rosario
• Idioma: eng
• OAI Identifier: oai:repository.urosario.edu.co:10336/22559
• Acceso en línea: https://doi.org/10.3934/mbe.2019171; https://repository.urosario.edu.co/handle/10336/22559
• Palabra clave: Decay (organic); Depolarization; Excited states; Laplace transforms; Neurons; Stochastic systems; Time switches; Asymptotical behaviour; First passage time; Laplace transform techniques; Membrane potentials; Neural activity; Neural modeling; Neuronal model; State-dependent; Stochastic models; Article; Depolarization; Excitation; Laplace transform; Membrane potential; Nerve cell; Probability; Stochastic model; Asymptotical behaviour; Firing probability; First passage time; Jump-telegraph process; Neural activity
• License: Abierto (Texto Completo)