Open AccessBifurcation analysis of complex behavior in the Logistic map via periodic impulsive force
Author(s) -
Haibo Jiang,
Tao Li,
Zeng Xiao-Liang,
Liping Zhang
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.120508
Subject(s) - bifurcation , logistic map , chaotic , floquet theory , period doubling bifurcation , complex dynamics , bifurcation theory , periodic orbits , statistical physics , mathematics , mathematical analysis , physics , control theory (sociology) , nonlinear system , computer science , artificial intelligence , control (management) , quantum mechanics
The complex dynamics of the Logistic map via two types of periodic impulsive forces is investigated in this paper. With the parameter varying, the system produces the phenomenon such as equilibrium solutions, periodic solutions, and chaotic solutions. Furthermore the system can evolve into chaos by a cascading of period-doubling bifurcations. The Poincaré map of the Logistic map via periodic impulsive force is constructed and its bifurcation is analyzed. Finally, the Floquet theory is used to explore the bifurcation mechanism for the periodic solutions.