Synchronization and Non-Smooth Dynamical Systems - Llibre, Jaume; da Silva, Paulo R. [UNESP]; Teixeira, Marco A. (Springer, 2012)
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 synchronizationwhich 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.
Keywords: Regularization; Vector field; Constrained system; Singular perturbation; Non-smooth vector field; Sliding vector field; Synchronization