Open AccessBifurcation of the critical crossing cycle in a planar piecewise smooth system with two zones
Author(s) -
Fang Wu,
Lihong Huang,
Jiafu Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021264
Subject(s) - mathematics , gravitational singularity , piecewise , tangent , bifurcation , planar , codimension , function (biology) , mathematical analysis , pure mathematics , class (philosophy) , geometry , combinatorics , physics , nonlinear system , computer science , computer graphics (images) , quantum mechanics , evolutionary biology , artificial intelligence , biology
In this paper, we consider the nonsmooth bifurcation around a class of critical crossing cycles, which are codimension-2 closed orbits composed of tangency singularities and regular orbits, for a two-parameter family of planar piecewise smooth system with two zones. By the construction of suitable displacement function (equivalently, Poincar \begin{document}$ {\rm\acute{e}} $\end{document} map), the stability and the existence of periodic solutions under the variation of the parameters inside this system are characterized. More precisely, we obtain some parameter regions on the existence of crossing cycles and sliding cycles near those loops. As applications, several examples are given to illustrate our main conclusions.