Synchronization and Non-Smooth Dynamical Systems

Jaume Llibre, Paulo R. da Silva, Marco A. Teixeira

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1 Citation (Scopus)


In this article we establish an interaction between non-smooth systems, geometric singular perturbation theory and synchronization phenomena. We find conditions for a non-smooth vector fields be locally synchronized. Moreover its regularization provide a singular perturbation problem with attracting critical manifold. We also state a result about the synchronization which occurs in the regularization of the fold-fold case. We restrict ourselves to the 3-dimensional systems (ℓ = 3) and consider the case known as a T-singularity. © 2012 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)1-12
JournalJournal of Dynamics and Differential Equations
Issue number1
Publication statusPublished - 1 Mar 2012


  • Constrained system
  • Non-smooth vector field
  • Regularization
  • Singular perturbation
  • Sliding vector field
  • Synchronization
  • Vector field


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