TY - JOUR
T1 - An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations
AU - Zhang , Qing
AU - Du , Zhengdong
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 759
EP - 774
PY - 2024
DA - 2024/08
SN - 6
DO - http://doi.org/10.12150/jnma.2024.759
UR - https://global-sci.org/intro/article_detail/jnma/23361.html
KW - Piecewise linear system, crossing limit cycle, piecewise linear perturbation, piecewise smooth switching curve, stability.
AB - <p style="text-align: justify;">In this paper, we present an example of piecewise linear systems
with infinitely many crossing limit cycles defined in two zones separated by
a piecewise linear curve with countable corners. Then we prove that under
piecewise linear perturbations, the perturbed system can have infinitely many
limit cycles, or exactly $ℓ$ limit cycles for any given nonnegative integer $ℓ.$</p>