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 …

A general mechanism to generate three limit cycles in planar Filippov systems with two zones

E Freire, E Ponce, F Torres - Nonlinear Dynamics, 2014 - Springer
Discontinuous piecewise linear systems with two zones are considered. A general canonical
form that includes all the possible configurations in planar linear systems is introduced and …

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 …

Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems

DJW Simpson - Physics Reports, 2022 - Elsevier
For many physical systems the transition from a stationary solution to sustained small
amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts …

Existence of limit cycles in general planar piecewise linear systems of saddle–saddle dynamics

SM Huan, XS Yang - Nonlinear Analysis: Theory, Methods & Applications, 2013 - Elsevier
The existence and number of limit cycles in a class of general planar piecewise linear
systems constituted by two linear subsystems with saddle–saddle dynamics are …

[HTML][HTML] On the number of limit cycles in general planar piecewise linear systems of node–node types

SM Huan, XS Yang - Journal of Mathematical Analysis and Applications, 2014 - Elsevier
We investigate the existence and number of limit cycles in a class of general planar
piecewise linear systems constituted by two linear subsystems with node–node dynamics …

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 …

Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation

J Llibre, MA Teixeira, J Torregrosa - International Journal of …, 2013 - World Scientific
In this paper, we provide a lower bound for the maximum number of limit cycles of planar
discontinuous piecewise linear differential systems defined in two half-planes separated by …

[HTML][HTML] Uniqueness of limit cycles for sewing planar piecewise linear systems

JC Medrado, J Torregrosa - Journal of Mathematical Analysis and …, 2015 - Elsevier
This paper proves the uniqueness of limit cycles for sewing planar piecewise linear systems
with two zones separated by a straight line, Σ, and only one Σ-singularity of monodromic …