TY - JOUR
T1 - Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium
AU - Liu, Xingbo
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - In this paper, bifurcations of heterodimensional cycle with one nonhyperbolic equilibrium and one saddle-focus in three-dimensional vector fields are investigated. We study the interaction of a transcritical bifurcation with a codimension-0/codimension-2 heteroclinic cycle. Based on the construction of a Poincaré return map, we obtain the expressions of parametric curves of homoclinic and heteroclinic connections around the heterodimensional cycle as well as periodic orbits. Furthermore, the configurations of the parametric curves corresponding to different bifurcations are illustrated.
AB - In this paper, bifurcations of heterodimensional cycle with one nonhyperbolic equilibrium and one saddle-focus in three-dimensional vector fields are investigated. We study the interaction of a transcritical bifurcation with a codimension-0/codimension-2 heteroclinic cycle. Based on the construction of a Poincaré return map, we obtain the expressions of parametric curves of homoclinic and heteroclinic connections around the heterodimensional cycle as well as periodic orbits. Furthermore, the configurations of the parametric curves corresponding to different bifurcations are illustrated.
KW - Heterodimensional cycle
KW - Poincaré map
KW - global bifurcation
KW - transcritical bifurcation
UR - https://www.scopus.com/pages/publications/85042774361
U2 - 10.1142/S0218127418500037
DO - 10.1142/S0218127418500037
M3 - 文章
AN - SCOPUS:85042774361
SN - 0218-1274
VL - 28
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 1
M1 - 8500037
ER -