Fluctuations and Correlations in the Bak-Sneppen Model
Received date: 2002-04-16
Revised date: 2002-06-11
Online published: 2003-03-10
Supported by
supported in part by National Natural Science Foundation under grant(10075035)
讨论关于自组织临界性的Bak-Sneppen模型中的涨落与关联.通过引入系统的平均适应性,从涨落中发现了系综平均后的适应性对格点大小的依赖性,并利用这种依赖性得到了间距方程的解及临界指数.讨论了演化过程中最小适应值的位置的跳变.在演化中,跳变的距离的分布在零值处越来越突出,这表明相邻两次更新中的最小适应值的位置间的关联越来越强.将最小适应值位置的跳变与一种时空关联联系起来,并得到了一个关联函数的简单表达式.
关键词： Bak-Sneppen模型; 涨落; 关联
杨纯斌 . Bak-Sneppen模型中的涨落与关联(英文)[J]. 中国科学院大学学报, 2003 , 20(2) : 187 -190 . DOI: 10.7523/j.issn.2095-6134.2003.2.010
The fluctuations and correlations in the Bak-Sneppen model for self-organized criticality are discussed. By introducing the mean fitness of the system, one can discover the lattice size dependence of the ensemble-averaged fitness from the fluctuations. From the size dependence one can find a solution of the gap-equation and then get the exponents for the model. We also investigate the flying of the minimum site in the updating process. The distribution of the fly distance becomes more and more sharp at 0, which shows the increase of the correlation between the minimum sites at two successive updates. We link a spatial-temporal correlation function with the flying and get a simple expression for the correlation function.
Key words： Bak-Sneppen model; fluctuations; correlations
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