在z-逻辑地图中,混乱边缘的中心极限行为
Abbas Ali Saberi1,2,3, Ugur Tirnakli4,5, Constantino Tsallis6,7,8
1Constructor University, School of Science, Campus Ring 1, 28759 Bremen, Germany.
Physical review. E
|January 21, 2026
概括
这项研究揭示了z-逻辑图的代汇聚到q-高斯分布. 提出了一个预测式的指数,q(z),并进行了数值验证.
科学领域:
- 复杂的系统复杂的系统.
- 统计力学 统计力学
- 动态系统 动态系统
背景情况:
- 费根姆-库莱特-特雷塞 (FCT) 点是混乱系统中的一个关键点.
- 一维地图,就像z-logistic地图一样,表现出复杂的行为.
研究的目的:
- 为了研究散散一维z-logistic图的代数的限制分布.
- 提出和验证一个预测式的热指数 (q).
主要方法:
- 在FCT点上分析z-物流图x_{t+1}=1-a
- 对q-高斯分布的收的证明.
- 使用数据崩进行数值验证.
主要成果:
- 代的总和汇聚到 q-高斯分布中,这些分布优化了非增值的热函数 S_q.
- 为热指数提出了一个封闭形式的预测,q(z) =1+2/(z+1),并进行了数值验证.
- 该研究确定了有限 (z>2) 和分歧 (1≤z≤2) 变异的条件.
结论:
- 这些发现将混乱边缘的中心极限行为扩展到标准物流图 (z=2) 以外.
- 为具有不同非线性顺序的单模地图建立了一个简单的预测定律.
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