Department of Mathematics

Dynamics of biological systems with multiple time-scales

Complex oscillations and waves in biological dynamical systems, arising from models with fast and slow variables.

Mathematical model depicting biological dynamical system

In many biological systems some processes occur much faster than others, and mathematical models of these systems therefore have multiple time-scales built into them. When trying to understand the complicated dynamics that may occur in models of this type, it is often useful to exploit the presence of the multiple timescales using a group of techniques called geometric singular perturbation theory (GSPT).

In this project, researchers at The University of Auckland, Sydney University and Bristol University are applying GSPT to mathematical models of calcium dynamics and other biological systems. We are particularly interested in the occurrence of complex oscillations and waves in these models. Our goal is to understand the phenomena that give rise to and control the complicated dynamics observed, with our long term aim being to design experiments that could distinguish between competing hypotheses.

Researchers at The University of Auckland



         National Institutes of Health, Laboratory of Biological Modeling

          University of Exeter, College of Engineering, Mathematics and Physical Sciences