Open AccessThe number of limit cycles by perturbing a piecewise linear system with three zones
Author(s) -
Xiaolei Zhang,
Yanqin Xiong,
Yi Zhang
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2022049
Subject(s) - mathematics , limit cycle , piecewise , limit (mathematics) , homoclinic orbit , piecewise linear function , bifurcation , function (biology) , mathematical analysis , hamiltonian (control theory) , homoclinic bifurcation , combinatorics , pure mathematics , physics , nonlinear system , quantum mechanics , mathematical optimization , evolutionary biology , biology
First, this paper provides a new proof for the expression of the generalized first order Melnikov function on piecewise smooth differential systems with multiply straight lines. Then, by using the Melnikov function, we consider the limit cycle bifurcation problem of a 3-piecewise near Hamiltonian system with two switching lines, obtaining \begin{document}$ 2n+3[\frac{n+1}{2}] $\end{document} limit cycles near the double generalized homoclinic loop.