Identification of relaxation oscillations - NNF grant to Elisenda Feliu

Sustained oscillations, that is, periodic responses of a system with respect to time, are prevalent in cell biology and play critical roles in cellular dynamics. Determining when a system displays oscillatory behaviour is a challenging task, which is often addressed by two strategies: either finding a Hopf bifurcation or identifying time-scale separations leading to relaxation oscillations.

Relaxation oscillations are typically found using case-specific approaches, and no black-box methods are known. The project focuses on differential equations arising from the study of biochemical reaction networks. It aims at identifying characteristics of the networks that are necessary for them to have relaxation oscillations.

The idea is that relaxation oscillations necessitate the existence of a type of algebraic variety with specific stability properties. Hence, the project focuses on determining when this algebraic variety can be found. The project will therefore contribute to the development of a systematized approach towards the identification of relaxation oscillations.

The research grant will finance the employment of a postdoc for two years. He or she will work in the research group of Elisenda Feliu, together with a PhD student, financed by Independent Research Fund Denmark, who studies Hopf bifurcations - also using algebraic approaches.

Associate Professor Elisenda Feliu is a leading member of the department’s research group Mathematical Biology. Elisenda has previously received research funding from the Novo Nordisk Foundation as well as Lundbeck Fonden and a Sapere Aude Starting Grant from Independent Research Fund Denmark.

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