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. ...

This paper is concerned with some aspects of the qualitative-geometric theory of non-smooth systems. We present a survey of the state of the art on the connection between the regularization process of nonsmooth vector ...

In this paper we study the maximum number N of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number ...

This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some ...

A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x', y') = (-y + epsilon f(x, y, epsilon), x + epsilon g(x, y, epsilon)). In this paper we study the limit cycles that bifurcate ...

In this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form x˙=1,(y˙)2={g1(x,y)ifφ(x,y)≥0g2(x,y)ifφ(x,y)≤0,where g1, g2, φ: U→ R are smooth ...