标题： 有限随机多米诺自动机 显示英文标题

标题： Finite Random Domino Automaton

摘要： 有限版本的随机多米诺自动机（FRDA）——最近提出的一种地震玩具模型——被研究。 分别推导出描述FRDA稳态的方程组，并与无限情况进行比较。 结果显示，对于大尺寸系统，这些方程与RDA方程一致。 我们证明了当尺寸N大于4时不存在精确方程，并提出了适当的近似方法，其质量在马尔可夫链框架下获得的例子中进行了研究。 我们推导出几个描述自动机特性的精确公式，包括时间方面。 特别是，提出了一种实现类似RDA准周期行为的方法。 因此，基于相同的微观规则——产生指数和反幂律分布——我们将该模型的应用范围扩展到准周期现象。 显示英文摘要

摘要： Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown that for the system of big size, these equations are coincident with RDA equations. We demonstrate a non-existence of exact equations for size N bigger then 4 and propose appropriate approximations, the quality of which is studied in examples obtained within Markov chains framework. We derive several exact formulas describing properties of the automaton, including time aspects. In particular, a way to achieve a quasi-periodic like behaviour of RDA is presented. Thus, based on the same microscopic rule - which produces exponential and inverse-power like distributions - we extend applicability of the model to quasi-periodic phenomena.