TY - JOUR
T1 - Bifurcation Analysis of a Class of Planar Piecewise Smooth Linear-Quadratic System
AU - Xiu , Qiwen
AU - Pi , Dingheng
JO - Annals of Applied Mathematics
VL - 3
SP - 282
EP - 308
PY - 2021
DA - 2021/01
SN - 36
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/18594.html
KW - piecewise smooth systems, limit cycle, sliding cycle, pseudo-homoclinic bifurcation, critical crossing bifurcation $CC$.
AB - <p style="text-align: justify;">In this paper, we consider a planar piecewise smooth differential system
consisting of a linear system and a quadratic Hamiltonian system. The quadratic system has some folds on the discontinuity line. The linear system may have
a focus, saddle or node. Our results show that this piecewise smooth differential
system will have two limit cycles and a sliding cycle. Moreover, this piecewise
smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation
and critical crossing bifurcation $CC$. Some examples are given to illustrate our
results.</p>