A Systematic Study of Stochastic Models in Neuronal Dynamics

• Grant number: 25/08274-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Victor de Angeli Dalarmi
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project proposes a systematic study of stochastic models applied to neuronal firing dynamics, with a focus on first-passage times. It will analyze both classical models and recent generalizations based on diffusion processes with and without jumps, such as Ornstein-Uhlenbeck, Feller, and Jacobi processes with non-local jumps. The goal is to compare the ability of each model to represent relevant physiological phenomena, such as the regularity and frequency of membrane potential spikes, aiming to understand how different mathematical structures affect the modeling of neuronal electrical activity. The project also aims to introduce the student to interdisciplinary scientific research at the interface of mathematics, neuroscience, and biophysical modeling.