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arXiv 2212.01459nlin.CD
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后勤地图上的模式:后到前

Patterns on logistic map: back to front

João Valle, Odemir M. Bruno

摘要:

最近,在混沌状态下的逻辑斯蒂映射轨道中发现了最低有效位的模式。然而,这些数字的动态并没有深入探讨。我们提出了一个新的解释的模式中发现的最低有效位数的Logistic映射在混沌政权,探索数字的动力学的基础上。我们探索了这些数字的动态迭代方法的低位。当探索最低有效位的动态时,发现周期和固定位与离散系统的固定和周期点的动态模拟。周期数表示已确定的周期大小,与参数控制或初始条件无关。固定数字具有吸引力和稳定性特征,例如固定点。这一分析表明,逻辑斯蒂映射的最低有效位具有特征动态。

英文摘要:

Recently patterns were found in the least significant digits in the logistic map orbits in the chaotic regime. However, the dynamic of these digits was not explored in deep. We propose a new interpretation of the patterns found in the least significant digits of the logistic map in a chaotic regime, based on exploring the digits' dynamics. We explored these digits by the dynamic iteration method for low positions. When the dynamic of the least significant digits was explored, periodic and fixed digits were found with dynamic analogs to fixed and periodic points of discrete systems. Periodic digits designated well-established period sizes, which are independent of parameter control or initial condition. Fixed digits have attraction and stability characteristics, such as fixed points. This analysis demonstrates that the logistic map's least significant digits have characteristic dynamics.

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