2020/06/17 by Jawher Jerray, Laurent Fribourg, Jerray, Jawher +3
Computer Science · Engineering · Physics and Astronomy · #FOS: Electrical engineering #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2006.09993
arxiv created 2020/06/17 · openalex publication_date 2020/06/17 · arxiv updated 2020/06/18 · openalex created_date 2020/06/25 · openalex updated_date 2026/07/28
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 S of the state space, and shows that any solution starting at S returns to S within a fixed number of periods k. 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.