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首页> 外文期刊>International Journal of Modern Physics, B. Condensed Matter Physics, Statistical Physics, Applied Physics >Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126
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Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126

机译：基于基本元胞自动机规则126的父级数可变的异步随机布尔网络模型

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摘要

A Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which can vary from one node to another, is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in "Asynchronous Random Boolean Network Model Based on Elementary Cellular Automata Rule 126", Phys. Rev. E 71, 026 232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be the same for all the nodes. We provide a model for the probability of finding a node in state 1 at a time t for the class of generalized asynchronous random Boolean networks (GARBN) in which a random number of nodes can be updated at each time point. We generate consecutive states of the network for both the real system and the models under the various schemes, and use simulation algorithms to show that the results match well. We use the model to study the dynamics of the system through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the GARBN's dynamics range from order to chaos, depending on the type of random variable generating the asynchrony and the parameter combinations.
机译：考虑一个具有N个节点的布尔网络，每个节点在时间t的状态由一定数量的父节点确定，该父节点可能在一个节点之间变化。这是Matache和Heidel在Phys的“基于基本元胞自动机规则126的异步随机布尔网络模型”中对于恒定数量的父节点获得的先前结果的概括。修订版E 71，026 232，2005。基于各种异步方案更新具有随机分配的邻域的节点。布尔规则是基本细胞自动机规则126的一般化，并且假定对于所有节点都相同。我们为广义异步随机布尔网络（GARBN）类提供了一个在时间t处找到状态1的节点的概率的模型，其中可以在每个时间点更新随机数的节点。我们在各种方案下为实际系统和模型生成网络的连续状态，并使用仿真算法来证明结果匹配良好。我们使用该模型通过对初始值，分叉图和定点分析的敏感性来研究系统的动力学。我们表明，GARBN的动态范围从阶到混沌，取决于生成异步和参数组合的随机变量的类型。

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