Dynamical analysis of DOG wavelet mapping with dilation and translation
Bocheng Bao, Hu Wen, Zhu-Sheng Kang, zhong hai liu, XU Jian-ping, (1)电子科技大学电子工程学院，成都 610054; (2)南京理工大学电子工程系，南京 210094; (3)南京理工大学电子工程系，南京 210094；江苏技术师范学院电气信息工程学院，常州 213001; (4)南京理工大学电子工程系，南京 210094；南京航空航天大学信息科学与技术学院，南京 210016; (5)西南交通大学电气工程学院，成都 610031 · Acta Physica Sinica · 2009
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 curves，its 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 behavior，bifurcation diagrams and Lyapunov spectra. Some nonlinear phenomena，such as period-doubling bifurcation，tangent bifurcation，boundary crisis bifurcation，periodic window，and imperfect Feigenbaum-tree，are revealed and investigated.