Synchronization and Non-Smooth Dynamical Systems

Abstract

Abstract. In this article we establish an interaction between nonsmooth 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 ( = 3) and consider the case known as a T-singularity.

Regularization of the Boundary Equilibrium Bifurcation in Filippov System with Rich Discontinuity Boundaries

“…In this work, we chose the method introduced by Sotomayor and Teixeira [27]. This method has already been applied to the case where the discontinuity boundary divides R 2 into two regions [28][29][30][31][32][33][34][35][36] and into four regions [11,14,37]. However, according to the authors' knowledge, they have not been applied to the case with three regions, which have more applications in reality.…”

Órbitas periódicas de certas equações diferenciais acopladas

“…Em [28] Llibre, Silva e Teixeira, assumindo a definição acima, estabeleceram conexões entre o fenômeno de sincronização, a teoria de sistemas dinâmicos descontínuos e a teoria geométrica de perturbação singular.…”