Guaranteed phase synchronization of hybrid oscillators using symbolic Euler's method: The Brusselator and biped examples
Abstract
The phenomenon of phase synchronization was evidenced in the 17th century by Huygens while observing two pendulums of clocks leaning against the same wall. This phenomenon has more recently appeared as a widespread phenomenon in nature, and turns out to have multiple industrial applications. The exact parameter values of the system for which the phenomenon manifests itself are however delicate to obtain in general, and it is interesting to find formal sufficient conditions to guarantee phase synchronization. Using the notion of reachability, we give here such a formal method. More precisely, our method selects a portion of the state space, and shows that any solution starting at returns to within a fixed number of periods . Besides, our method shows that the components of the solution are then (almost) in phase. We explain how the method applies on the Brusselator reaction-diffusion and the biped walker examples.
Cite
@article{arxiv.2006.09993,
title = {Guaranteed phase synchronization of hybrid oscillators using symbolic Euler's method: The Brusselator and biped examples},
author = {Jawher Jerray and Laurent Fribourg and Étienne André},
journal= {arXiv preprint arXiv:2006.09993},
year = {2020}
}