[HTML][HTML] The number and stability of limit cycles for planar piecewise linear systems of node–saddle type

J Wang, X Chen, L Huang - Journal of Mathematical Analysis and …, 2019 - Elsevier
The objective of this paper is to study the number and stability of limit cycles for planar
piecewise linear (PWL) systems of node–saddle type with two linear regions. Firstly, we give …

Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type

J Wang, C Huang, L Huang - Nonlinear Analysis: Hybrid Systems, 2019 - Elsevier
The aim of this paper is to deal with the problem of limit cycles for a general planar
piecewise linear differential system of saddle–focus type. By using the Liénard-like …

Maximum number of limit cycles for certain piecewise linear dynamical systems

J Llibre, DD Novaes, MA Teixeira - Nonlinear Dynamics, 2015 - Springer
This paper deals with the question of the determinacy of the maximum number of limit cycles
of some classes of planar discontinuous piecewise linear differential systems defined in two …

Limit cycles induced by threshold nonlinearity in planar piecewise linear systems of node-focus or node-center type

J Wang, S He, L Huang - International Journal of Bifurcation and …, 2020 - World Scientific
In this paper, we investigate limit cycles induced by threshold nonlinearity of piecewise
linear (PWL) differential systems, which are node-focus type or node-center type with the …

The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems

J Castillo, J Llibre, F Verduzco - Nonlinear Dynamics, 2017 - Springer
The creation or destruction of a crossing limit cycle when a sliding segment changes its
stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we …

[HTML][HTML] Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

J Llibre, X Zhang - Journal of Mathematical Analysis and Applications, 2018 - Elsevier
From the beginning of this century more than thirty papers have been published studying the
limit cycles of the discontinuous piecewise linear differential systems with two pieces …

Limit cycles in planar piecewise linear differential systems with nonregular separation line

PT Cardin, J Torregrosa - Physica D: Nonlinear Phenomena, 2016 - Elsevier
In this paper we deal with planar piecewise linear differential systems defined in two zones.
We consider the case when the two linear zones are angular sectors of angles α and 2 π− α …

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 …

Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones

R Euzebio, R Pazim, E Ponce - Physica D: Nonlinear Phenomena, 2016 - Elsevier
We consider continuous piecewise-linear differential systems with three zones where the
central one is degenerate, that is, the determinant of its linear part vanishes. By moving one …

[PDF][PDF] Limit cycle bifurcations in discontinuous planar systems with multiple lines

Y Xiong, M Han - J. Appl. Anal. Comput, 2020 - jaac-online.com
In this paper, the limit cycle bifurcation problem is investigated for a class of planar
discontinuous perturbed systems with n parallel switch lines. Under the assumption that the …