Stephanie Abo | Applied Math, University of Waterloo
Reduction of High-Dimension Models of Circadian Clocks to a Two-Dimension Manifold Representation
In this talk, I will present a model reduction technique applicable to oscillatory dynamical systems. The method is based on the projection of high-dimensional models onto their respective manifold using proper orthogonal functions (POF) obtained from the decomposition of the phase space of the model to obtain a 2-dimension model. The reduced model predicts most of the salient features of the original model. I will focus on the specific case of biological clocks characterized by oscillations of ~24 h. The manifold representation simplifies the mathematical analysis, since only 2 variables need to be observed and analyzed to understand the behavior of the biological clock.