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Guaranteed phase synchronization of hybrid oscillators using symbolic Euler's method (verification challenge)

12 pagesPublished: September 26, 2020

Abstract

The phenomenon of phase synchronization was evidenced in the 17th century by Huy- gens while observing two pendulums of clocks leaning against the same wall. This phe- nomenon 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. These examples can also be seen as “challenges” for the verification of continuous and hybrid systems.

Keyphrases: Biped walker, Brusselator, Euler method, hybrid system, phase synchronization, reachability, Reaction–diffusion system

In: Goran Frehse and Matthias Althoff (editors). ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20), vol 74, pages 197--208

Links:
BibTeX entry
@inproceedings{ARCH20:Guaranteed_phase_synchronization_of,
  author    = {Jawher Jerray and Laurent Fribourg and \textbackslash{}'Etienne Andr\textbackslash{}'e},
  title     = {Guaranteed phase synchronization of hybrid oscillators using symbolic Euler's method (verification challenge)},
  booktitle = {ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20)},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {74},
  pages     = {197--208},
  year      = {2020},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/lDgg},
  doi       = {10.29007/l3k2}}
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