极端混沌布尔网络
Extremely chaotic Boolean networks
摘要：
研究网络结构的条件以保证其底层动力系统的给定行为是一个越来越重要的问题。在本文中，我们报告说，一个布尔网络可能属于混沌政权，即使在同时假设的几个条件下，在随机研究已分别显示与有序行为。这些特性包括每个变量最多使用两个输入，使用有偏和canalyzing调节函数，以及限制负反馈回路的数量。我们还证明了对于n维布尔网络，如果每个变量的输出数是有界的，并且存在长度为c^n的周期轨道，c足够接近2，则任何具有这些性质的网络都必须有很大比例的变量简单地复制其他变量的先前值。这种系统与作用于一个或多个磁带的相对较小的图灵机共享结构相似性。
英文摘要：
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic regime, even under the simultaneous assumption of several conditions which in randomized studies have been separately shown to correlate with ordered behavior. These properties include using at most two inputs for every variable, using biased and canalyzing regulatory functions, and restricting the number of negative feedback loops. We also prove for n-dimensional Boolean networks that if in addition the number of outputs for each variable is bounded and there exist periodic orbits of length c^n for c sufficiently close to 2, any network with these properties must have a large proportion of variables that simply copy previous values of other variables. Such systems share a structural similarity to a relatively small Turing machine acting on one or several tapes.
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