TY - JOUR
T1 - Degenerate bifurcations of heterodimensional cycles with orbit flip
AU - Liu, Xingbo
AU - Liu, Junying
AU - Zhu, Deming
PY - 2013/5
Y1 - 2013/5
N2 - In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic orbits and the heterodimensional cycle are studied, the relevant bifurcation surfaces and their existing regions are given. Some known results are extended. An example is given to show the existence of the system which has a heterodimensional cycle with orbit flip.
AB - In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic orbits and the heterodimensional cycle are studied, the relevant bifurcation surfaces and their existing regions are given. Some known results are extended. An example is given to show the existence of the system which has a heterodimensional cycle with orbit flip.
KW - Bifurcation
KW - heterodimensional cycle
KW - local coordinates
KW - orbit flip
UR - https://www.scopus.com/pages/publications/84878903870
U2 - 10.1142/S0218127413500806
DO - 10.1142/S0218127413500806
M3 - 文章
AN - SCOPUS:84878903870
SN - 0218-1274
VL - 23
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 5
M1 - 1350080
ER -