
Mathematical tools for the analysis of oscillators
Jorge Goncalves 
Department of Engineering, University of Cambridge , UK 
This talk describes several mathematical tools that can help better understand limit cycles such as circadian oscillators. In addition to biologist’s intuition and knowledge of a system, such tools ranging from system identification to stability and robustness analysis can help to find and explain fundamental mechanisms in oscillators. The talk focuses on three major topics. (1) Through a case study of the circadian clock in /Arabidopsis/, it shows some recent discoveries of new components and feedback loops using system identification tools. Then (2) using several models of circadian oscillators it illustrates how linear tools can decompose the system in modes that simplify and model reduce complex systems. Finally (3), it addresses synchronisation of oscillators showing how both simulation and analysis can help explain the complex mechanisms behind synchronisation.