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Global Analysis and Synthesis of Oscillations


Dynamical systems that exhibit robust nonlinear oscillations are called oscillators. Oscillators are ubiquitous in physical, biological, biochemical, and electromechanical systems. Detailed models of oscillators abound in the literature, most frequently in the form of a set of nonlinear differential equations whose solutions robustly converge to a limit cycle oscillation. The lack of general analysis methods generally forces models of oscillators to be studied through numerical simulation methods. Although numerical simulations of these models may give a first insight into their behaviour, a more in-depth understanding is generally impeded by the complexity of the models and the challenge of rigorous global stability, robustness, and sensitivity analysis. Th ese considerations show the need for developing a general method that allows the global analysis of oscillators, either isolated or interconnected. The development of such a method would allow for a better understanding of the fundamental mechanisms respon sible for oscillations in complex models of oscillators, or networks of interconnected oscillators. Results of this research find application in interdisciplinary fields like analysis of oscillations in biological and biochemical systems (like circadian rh ythms and gene metabolic networks), complex networked systems, economic markets models, and cybernetics (rhythmic tasks robots as, for example, walking robots). The proposed project is clearly multidisciplinary, mixing topics such as system modelling, nonl inear systems theory, numerical analysis and computer science. It will allow to combine the fellow's background in nonlinear systems theory and control, with the expertise of the host institution that is known to be very prestigious in numerical analysis a nd computer science. The new competencies acquired by the fellow during his stay in the host institution will be extremely useful to the development of his scientific career and future researches.

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The old schools, trinity lane
Reino Unido

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