关键词: 二维logistic映射, Hopf分岔, 关联维数, Kolmogorov熵, 逃逸时间算法, 广义M—J集

Abstract: The dynamic behaviors of the two-dimensional logistic system are analyzed and the fractal characterization of strange attractors is researched. By using phase maps, bifurcation graphics and Lyapunov exponent, the paper reveals the transition of two-dimensional logistic system from regularity to chaos. By using G-P algorithm, the correlation dimension and Kolmogorov entropy of strange attractors are calculated, so the fractal characterization of strange attractors is described qualitatively. By using escape time algorithm, the color general Mandelbrot-Julia sets of strange attractors are construeted, so the fractal characterization of strange attractors is described quantitatively. The results show that the fractal characterization of strange attractors is explained clearly when these methods are used altogether.

Key words: two-dimensional logistic system, Hopf bifurcation, correlation dimension, Kolmogorov entropy, escape time algorithm, general Mandelbrot-Julia sets