TY - JOUR
T1 - Polynomial maps with hidden complex dynamics
AU - Zhang, Xu
AU - Chen, Guanrong
PY - 2019/6
Y1 - 2019/6
N2 - The dynamics of a class of one-dimensional polynomial maps are studied, and interesting dynamics are observed under certain conditions: the existence of periodic points with even periods except for one fixed point; the coexistence of two attractors, an attracting fixed point and a hidden attractor; the existence of a double period-doubling bifurcation, which is different from the classical period-doubling bifurcation of the Logistic map; the existence of Li-Yorke chaos. Furthermore, based on this one-dimensional map, the corresponding generalized Hénon map is investigated, and some interesting dynamics are found for certain parameter values: the coexistence of an attracting fixed point and a hidden attractor; the existence of Smale horseshoe for a subshift of finite type and also Li-Yorke chaos.
AB - The dynamics of a class of one-dimensional polynomial maps are studied, and interesting dynamics are observed under certain conditions: the existence of periodic points with even periods except for one fixed point; the coexistence of two attractors, an attracting fixed point and a hidden attractor; the existence of a double period-doubling bifurcation, which is different from the classical period-doubling bifurcation of the Logistic map; the existence of Li-Yorke chaos. Furthermore, based on this one-dimensional map, the corresponding generalized Hénon map is investigated, and some interesting dynamics are found for certain parameter values: the coexistence of an attracting fixed point and a hidden attractor; the existence of Smale horseshoe for a subshift of finite type and also Li-Yorke chaos.
KW - Attractor
KW - bifurcation
KW - Li-Yorke chaos
KW - polynomial map
KW - Smale horseshoe
KW - GENERALIZED HENON MAPS
KW - LORENZ
KW - DIFFEOMORPHISMS
UR - http://www.scopus.com/inward/record.url?scp=85061440134&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85061440134&origin=recordpage
U2 - 10.3934/dcdsb.2018293
DO - 10.3934/dcdsb.2018293
M3 - RGC 21 - Publication in refereed journal
SN - 1531-3492
VL - 24
SP - 2941
EP - 2954
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 6
ER -