Open AccessDynamical analysis of DOG wavelet mapping with dilation and translation
Author(s) -
Bocheng Bao,
Hao Wen,
Kang Zhu-Sheng,
Zhong Liu,
Jianping Xu
Publication year - 2009
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.58.2240
Subject(s) - tangent , dilation (metric space) , bifurcation diagram , fixed point , bifurcation , wavelet , mathematical analysis , mathematics , period doubling bifurcation , nonlinear system , bifurcation theory , physics , geometry , computer science , quantum mechanics , artificial intelligence
A 1-D smooth map constructed from DOG wavelet function is discussed in this paper. With analysis on the fixed points and the constructed iterative curvesits dynamical characteristics are thoroughly studied. It is found that the number of the fixed points will increase or decrease depending on the dilation and translation operation of the wavelet and thus the stable or unstable cross points and tangent point or zero points are produced. Numerical calculations are performed to obtain the dynamic behaviorbifurcation diagrams and Lyapunov spectra. Some nonlinear phenomenasuch as period-doubling bifurcationtangent bifurcationboundary crisis bifurcationperiodic windowand imperfect Feigenbaum-treeare revealed and investigated.