We develop the averaging theory of first and second order for studying the periodic solutions
of discontinuous piecewise differential systems in arbitrary dimension and with an arbitrary …

In this paper, we study Poincaré, Hopf and homoclinic bifurcations of limit cycles for planar
near-Hamiltonian systems. Our main results establish Hopf and homoclinic bifurcation …

A new result on averaging theory for a class of discontinuous planar differential systems with
applications Page 1 Rev. Mat. Iberoam. 33 (2017), no. 4, 1247–1265 doi 10.4171/rmi/970 c …

In this paper we develop an arbitrary order Melnikov function to study limit cycles bifurcating
from a periodic submanifold for autonomous piecewise smooth differential systems in R n …

We study the family of piecewise linear differential systems in the plane with two pieces
separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number …

This work is devoted to study the existence of periodic solutions for a class of ε-family of
discontinuous differential systems with many zones. We show that the averaged functions at …

In this paper, we are interested in providing lower estimations for the maximum number of
limit cycles H (n) that planar piecewise linear differential systems with two zones separated …

In this work we first provide sufficient conditions to assure the persistence of some zeros of
functions having the form $\begin {align*}\newcommand {\e}{\varepsilon}\newcommand …

Let p be a uniform isochronous cubic polynomial center. We study the maximum number of
small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding …

We consider the well-known Sprott A system, which is a special case of the widely studied
Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable …