TY - JOUR
T1 - Bifurcations of multiple homoclinics in general dynamical systems
AU - Xu, Yancong
AU - Zhu, Deming
AU - Liu, Xingbo
PY - 2011/7
Y1 - 2011/7
N2 - By using the local active coordinates consisting of tangent vectors of the invariant subspaces, as well as the Silnikov coordinates, the simple normal form is established in the neighborhood of the double homoclinic loops with bellows configuration in a general system, then the dynamics near the homoclinic bellows is investigated, and the existence, uniqueness of the homoclinic orbits and periodic orbits with various patterns bifurcated from the primary orbits are demonstrated, and the corresponding bifurcation curves (or surfaces) and existence regions are located.
AB - By using the local active coordinates consisting of tangent vectors of the invariant subspaces, as well as the Silnikov coordinates, the simple normal form is established in the neighborhood of the double homoclinic loops with bellows configuration in a general system, then the dynamics near the homoclinic bellows is investigated, and the existence, uniqueness of the homoclinic orbits and periodic orbits with various patterns bifurcated from the primary orbits are demonstrated, and the corresponding bifurcation curves (or surfaces) and existence regions are located.
KW - Bifurcations
KW - Homoclinic bellows
KW - Silnikov coordinates
UR - https://www.scopus.com/pages/publications/79954562293
U2 - 10.3934/dcds.2011.30.945
DO - 10.3934/dcds.2011.30.945
M3 - 文章
AN - SCOPUS:79954562293
SN - 1078-0947
VL - 30
SP - 945
EP - 963
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 3
ER -