arXiv 1503.086852015-03-30cond-mat.stat-mechnlin.CD

混沌边缘的耦合Logistic映射

A closer look at coupled logistic maps at the edge of chaos

Ugur Tirnakli, Constantino Tsallis

备注：: 7 pages, 9 figs

摘要：

我们专注于一个线性链的$N$第一邻居耦合的Logistic映射在其混沌的边缘存在一个共同的噪声。该模型由耦合强度$ε$和噪声宽度$σ_{max}$表征，最近由Pluchino等人[Phys. Rev. E { \bf 87}，022910（2013）]引入。他们发现，时间平均回报率与特征回报时间$τ$，可能的连接与$q$ -高斯，分布优化，在适当的约束下，非加性熵$S_q$，非广泛的统计力学的基础。在这里，我们仔细研究了这个模型，并在数值上获得的概率分布，表现出轻微的不对称的一些参数值，在方差与简单的$q$ -高斯。然而，沿着几十年来，与$q$ -高斯拟合原来是数值上非常令人满意的参数值的宽区域，我们说明了如何指数$q$演变与$(N, τ, ε, σ_{max})$。然而，在进行这样的数值分析时必须多么小心，这是有启发性的。整体工作表明，物理和/或生物系统，正确地模仿Pluchino等人的模型是热统计相关的非广泛的统计力学时，时间平均的相关量进行了研究。

英文摘要：

We focus on a linear chain of $N$ first-neighbor-coupled logistic maps at their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength $ε$ and the noise width $σ_{max}$, was recently introduced by Pluchino et al [Phys. Rev. E {\bf 87}, 022910 (2013)]. They detected, for the time averaged returns with characteristic return time $τ$, possible connections with $q$-Gaussians, the distributions which optimise, under appropriate constraints, the nonadditive entropy $S_q$, basis of nonextensive statistics mechanics. We have here a closer look on this model, and numerically obtain probability distributions which exhibit a slight asymmetry for some parameter values, in variance with simple $q$-Gaussians. Nevertheless, along many decades, the fitting with $q$-Gaussians turns out to be numerically very satisfactory for wide regions of the parameter values, and we illustrate how the index $q$ evolves with $(N, τ, ε, σ_{max})$. It is nevertheless instructive on how careful one must be in such numerical analysis. The overall work shows that physical and/or biological systems that are correctly mimicked by the Pluchino et al model are thermostatistically related to nonextensive statistical mechanics when time-averaged relevant quantities are studied.

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英文摘要：

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