“从有序到混沌”瞬时转换的差分格式

2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775) Pub Date : 2003-08-20 DOI:10.1109/PHYCON.2003.1236864

A.F. Goloubentsev, V. M. Anikin, Y.A. Barulina

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引用次数: 0

摘要

在无限区间上构造了一阶依赖于某参数的一维非线性差分方程。它的精确解具有半群性质，在参数变化的各个区域表现出规则或混沌的行为。有一个参数值“提供”一个“从有序到混乱”的瞬间转换。混沌状态的特征是具有柯西分布形式的不变密度和正Lyapunov指数In2。给出了构造映射的Perron-Frobenius算子的特征函数和特征值。

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Difference scheme with instant transition "from order to chaos"

The one-dimensional nonlinear difference equation of the first order depending on a parameter is constructed on the infinite interval. Its exact solutions have semi-group properties and demonstrate regular or chaotic behavior for various regions of parameter changing. There is a parameter value that "provides" an instant transition "from order to chaos". The chaotic regime is characterized by having the invariant density in the form of the Cauchy distribution and the positive Lyapunov exponent In2. The eigenfunction and eigenvalues of the Perron-Frobenius operator for constructed map are found.

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来源期刊

2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775)

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