TY - JOUR
T1 - Melnikov Functions for a Class of Piecewise Hamiltonian Systems
AU - Hou , Wenwen
AU - Liu , Shanshan
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 123
EP - 145
PY - 2023
DA - 2023/08
SN - 5
DO - http://doi.org/10.12150/jnma.2023.123
UR - https://global-sci.org/intro/article_detail/jnma/21921.html
KW - Piecewise smooth system, Melnikov function, Limit cycle, Bifurcation.
AB - <p style="text-align: justify;">This paper is concerned with the number of limit cycles for a
class of piecewise Hamiltonian systems with two zones separated by two semistraight lines. By constructing a Poincaré map, we obtain explicit expressions
of the first, second and third order Melnikov functions. In addition, we apply
their expressions to give upper bounds of the number of limit cycles bifurcated
from a period annulus of a piecewise polynomial Hamiltonian system.</p>