da Silva Marco Antonio Alves, Viswanathan G M, Ferreira A S, Cressoni J C
Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Apr;77(4 Pt 1):040101. doi: 10.1103/PhysRevE.77.040101. Epub 2008 Apr 8.
We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.
我们研究了一种最近提出的非马尔可夫随机游走模型，其特征是对近期过去的记忆丧失和遗忘诱导的持续性。我们报告了数值和分析结果，展示了该系统完整的相图，该相图由四个相组成：（i）经典非持续性，（ii）经典持续性，（iii）对数周期非持续性，以及（iv）由负反馈驱动的对数周期持续性。前两个相具有连续尺度不变性对称性，然而，对数周期性打破了这种对称性。相反，对数周期运动满足离散尺度不变性对称性，具有复分形维数而非实分形维数。我们发现，对于对数周期持续性，不仅有统计上的自相似性证据，还有几何上的自相似性证据。
