Wang Chuanfu, Ding Qun
Electronic Engineering College, Heilongjiang University, Harbin 150080, China.
Entropy (Basel). 2019 Jul 4;21(7):658. doi: 10.3390/e21070658.
When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic construction theory, the construction of chaotic systems mainly depends on the exhaustive search of systematic parameters or initial values, especially for a class of dynamical systems with hidden chaotic attractors. In this paper, a class of quadratic polynomial chaotic maps is studied, and a general method for constructing quadratic polynomial chaotic maps is proposed. The proposed polynomial chaotic maps satisfy the Li-Yorke definition of chaos. This method can accurately control the amplitude of chaotic time series. Through the existence and stability analysis of fixed points, we proved that such class quadratic polynomial maps cannot have hidden chaotic attractors.
当混沌系统应用于不同的实际场景，如混沌保密通信和混沌伪随机序列发生器时，对大量混沌系统有强烈需求。然而，由于缺乏系统的构建理论，混沌系统的构建主要依赖于对系统参数或初始值的穷举搜索，特别是对于一类具有隐藏混沌吸引子的动力系统。本文研究了一类二次多项式混沌映射，并提出了构建二次多项式混沌映射的通用方法。所提出的多项式混沌映射满足李 - 约克混沌定义。该方法能够精确控制混沌时间序列的幅度。通过对不动点的存在性和稳定性分析，我们证明了此类二次多项式映射不会有隐藏混沌吸引子。
