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Guaranteed phase synchronization of hybrid oscillators using symbolic Eulers method The Brusselator and biped examples

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Document pages: 12 pages

Abstract: The phenomenon of phase synchronization was evidenced in the 17th century byHuygens while observing two pendulums of clocks leaning against the same wall.This phenomenon has more recently appeared as a widespread phenomenon innature, and turns out to have multiple industrial applications. The exactparameter values of the system for which the phenomenon manifests itself arehowever delicate to obtain in general, and it is interesting to find formalsufficient conditions to guarantee phase synchronization. Using the notion ofreachability, we give here such a formal method. More precisely, our methodselects a portion $S$ of the state space, and shows that any solution startingat $S$ returns to $S$ within a fixed number of periods $k$. Besides, our methodshows that the components of the solution are then (almost) in phase. Weexplain how the method applies on the Brusselator reaction-diffusion and thebiped walker examples.

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