Jonathan Rubin, Multiple timescale modeling for neural systems

Abstract

Mathematical models of biological systems, including neurons, often feature components that evolve on very different timescales. Mathematical analysis of these multi-timescale systems can be greatly simplified by partitioning them into subsystems that evolve on different time scales. The subsystems are then analyzed semi-independently, using a technique called fast-slow analysis. I will briefly describe the fast-slow analysis technique and its application to neuronal bursting oscillations and basic coupled neuron modeling. After this, I will discuss fancier forms of dynamics such as canard oscillations, mixed-mode oscillations, and three-timescale dynamics. Although these examples all involve neural systems, the methods can and have been applied to other biological, chemical, and physical systems.