摘要翻译：
本文在Fokker-Planck方程的基础上，给出了最近[Cressoni et al.，Phys.Rev.Lett.98，070603(2007)和Sch\“Utz and Trimper，Phys.Rev.E70，045101(2004)]为Alzheimer行为和相关现象而引入的具有记忆的随机游动的解析公式，并给出了精确解。为此导出的时滞微分方程的解可以产生对数周期振荡，与以前发表的计算机模拟结果相当吻合。在此基础上，还构造了几个方向的推广。
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英文标题：
《Analytic Formulation, Exact Solutions, and Generalizations of the
  Elephant and the Alzheimer Random Walks》
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作者：
V. M. Kenkre
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  An analytic formulation of memory-possessing random walks introduced recently [Cressoni et al., Phys. Rev. Lett. 98, 070603 (2007) and Sch\"utz and Trimper, Phys. Rev. E 70, 045101 (2004)] for Alzheimer behavior and related phenomena is provided along with exact solutions on the basis of Fokker-Planck equations. The solution of a delay-differential equation derived for the purpose is shown to produce log-periodic oscillations and to coincide rather accurately with previously published computer simulation results. Generalizations along several directions are also constructed on the basis of the formalism.
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PDF链接：
https://arxiv.org/pdf/708.0034