The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line
M Esteban, J Llibre, C Valls - Chaos: An Interdisciplinary Journal of …, 2021 - pubs.aip.org
In this paper, we deal with discontinuous piecewise differential systems formed by two
differential systems separated by a straight line when these two differential systems are …
differential systems separated by a straight line when these two differential systems are …
Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones
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 …
discontinuous differential systems with many zones. We show that the averaged functions at …
The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems
R Benterki, J Llibre - Nonlinear Dynamics, 2020 - Springer
We provide the maximum number of limit cycles of some classes of discontinuous piecewise
differential systems formed by two differential systems separated by a straight line, when …
differential systems formed by two differential systems separated by a straight line, when …
Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields
In the present study, we consider planar piecewise linear vector fields with two zones
separated by the straight line x= 0. Our goal is to study the existence of simultaneous …
separated by the straight line x= 0. Our goal is to study the existence of simultaneous …
Limit cycles from a monodromic infinity in planar piecewise linear systems
Planar piecewise linear systems with two linearity zones separated by a straight line and
with a periodic orbit at infinity are considered. By using some changes of variables and …
with a periodic orbit at infinity are considered. By using some changes of variables and …
[HTML][HTML] Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
We consider an n-dimensional piecewise smooth vector field with two zones separated by a
hyperplane Σ which admits an invariant hyperplane Ω transversal to Σ containing a period …
hyperplane Σ which admits an invariant hyperplane Ω transversal to Σ containing a period …
Limit cycles of discontinuous piecewise differential Hamiltonian systems separated by a circle, or a parabola, or a hyperbola
JA Casimiro, J Llibre - Mathematics and Computers in Simulation, 2024 - Elsevier
Piecewise differential systems in the plane have been extensively studied in the last two
decades, due to the vast application of these systems to describe natural phenomena. The …
decades, due to the vast application of these systems to describe natural phenomena. The …
Limit cycles of generic piecewise center-type vector fields in R3 separated by either one plane or by two parallel planes
While the limit cycles of the piecewise differential systems in the plane R 2 have been
studied intensively during these last twenty years, this is not the case for the limit cycles of …
studied intensively during these last twenty years, this is not the case for the limit cycles of …
The 16th Hilbert Problem for Discontinuous Piecewise Linear Hamiltonian Saddles and Isochronous Centers Separated by a Straight Line
J Llibre, C Valls - Differential Equations and Dynamical Systems, 2024 - Springer
We provide the maximum number of limit cycles for discontinuous piecewise differential
systems separated by a straight line and formed by a linear Hamiltonian saddle and one of …
systems separated by a straight line and formed by a linear Hamiltonian saddle and one of …
Bifurcation of limit cycles at infinity in a class of switching systems
F Li, Y Liu, P Yu - Nonlinear Dynamics, 2017 - Springer
In this paper, we present a method to compute focal values and periodic constants at infinity
of a class of switching systems and apply it to study a cubic system. We prove that such a …
of a class of switching systems and apply it to study a cubic system. We prove that such a …