一个新的混沌映射及其算法实现

中文字数:7108,中文页数:13  英文字数:4690页数:16

 Abstract: a new chaotic mapping is given. An analytic expression and a few figures of the new chaotic mapping-meshy mapping are presented. A Comparison between the new chaos mapping and the classical Logistic mapping, Mandness curve and some abstractors coming from neural net is made. The behavior of the meshy mapping is analyzed from the viewpoint of graphics. A few illustrations are given. The most important significance of this discovery is that an approximate periodic is constructed by an aperiodic mapping. Otherwise, the result of this research is significant in its application and reference value in simulation of propagation and creating of fractal art. Moreover, it proposes a new approach for the research on chaos dynamics.
 
Keywords: chaos; Logistic mapping; fractal; Nonlinear systems

摘    要
 本文给出了一个新的混沌映射—网状映射的解析表达式及其图形，将其同传统的Logistic映射以及Mandness曲线、神经网络所产生的吸引子的图形进行了比较，从图形学的角度对其形态进行了分析。给出了由该网状混沌所派生出来的一些例子。本文的工作对利用分形进行动植物模拟以及分形艺术的创造有重要的参考意义和应用价值，对混沌动力系统的研究也提供了一种新的途径。

关键词  混沌    Logistic映射   分形     非线性系统

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