Disciplines
Biology (30%); Mathematics (70%)
Keywords
MIXED-MODE OSCILLATIONS,
CHEMICAL KINETICS,
NEURONAL MODELS,
GEOMETRIC SINGULAR PERTURBATION THEORY,
CANARD SOLUTIONS
Abstract
Mixed-mode oscillations (MMO) are one of the various patterns in the dynamics of chemical and physiological
processes. They owe their name to their alternating large and small amplitudes. In my previous project I
concentrated on systems modeled by a few coupled nonlinear ordinary differential equations. Now I want to study
MMOs in larger systems of ODEs as they are represented by coupled oscillators and MMOs in partial differential
equations. The basis for this will be a final clarification of the problem for the simple ODE case.