TY - JOUR
T1 - Bifurcations of Double Homoclinic Loops with Inclination Flip and Nonresonant Eigenvalues
AU - Jia , Qianqian
AU - Zhang , Weipeng
AU - Lu , Qiuying
AU - Li , Xiaodong
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 25
EP - 44
PY - 2021
DA - 2021/04
SN - 2
DO - http://doi.org/10.12150/jnma.2020.25
UR - https://global-sci.org/intro/article_detail/jnma/18796.html
KW - Double homoclinic loops, Nonresonant eigenvalues, Inclination
flip, Periodic orbit, Bifurcation.
AB - <p style="text-align: justify;">In this work, bifurcation analysis near double homoclinic loops
with $W^s$ inclination flip of $Γ_1$ and nonresonant eigenvalues is presented in a
four-dimensional system. We establish a Poincaré&nbsp;map by constructing local
active coordinates approach in some tubular neighborhood of unperturbed
double homoclinic loops. Through studying the bifurcation equations, we
obtain the condition that the original double homoclinic loops are persistent,
and get the existence or the nonexistence regions of the large 1-homoclinic
orbit and the large 1-periodic orbit. At last, an analytical example is given to
illustrate our main results.</p>