A geometric theory for non-standard relaxation oscillators

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This project aims to develop new geometric methods for the analysis of multi-scale models of biological rhythms, and design diagnostic tools to identify key parameters that cause and control these signals. Rhythms, such as breathing, neural and cardiac rhythms and pulsatile hormone secretion, are central for life. Many important biochemical cell signals exhibiting relaxation-type behaviour cannot be rigorously analysed with standard dynamical systems tools due to an inherent non-uniform time-scale splitting in these models. This project aims to develop a unified mathematical theory that weaves together results from geometric singular perturbation theory and algebraic geometry to explain the genesis of complex rhythms and patterns in biological, non-standard, multi-scale systems, both at individual and network level.