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A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to.  This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t.  This may be done synchronously or asynchronously.

A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to.  This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t.  This may be done synchronously or asynchronously.

'''<font color="#FF8000">布尔网络 Boolean Network </font>'''由一组离散的布尔变量组成，每个变量都被分配了一个布尔函数（可能每个变量都不同），它从这些变量的子集中获取输入，并输出决定其被分配的变量的状态。 这一组函数实际上决定了变量集上的拓扑结构（连通性），这些变量就成为网络中的节点。通常，系统的动态是以离散时间序列的形式进行的，通过评估每个变量在时间t的网络状态上的函数来确定整个网络在时间t+1的状态，这可能是同步或异步完成的。

'''<font color="#FF8000">布尔网络 Boolean Network </font>'''由一组离散的布尔变量组成，每个变量都被分配了一个布尔函数（可能每个变量都不同），它从这些变量的子集中获取输入，并输出决定其被分配的变量的状态。 这一组函数实际上决定了变量集上的拓扑结构（连通性），这些变量就成为网络中的节点。通常，系统的动态是以离散时间序列的形式进行的，通过评估每个变量在时间 ''t'' 的网络状态上的函数来确定整个网络在时间 ''t+1''的状态，这可能是同步或异步完成的。

Boolean networks have been used in biology to model regulatory networks. Although Boolean networks are a crude simplification of genetic reality where genes are not simple binary switches, there are several cases where they correctly capture the correct pattern of expressed and suppressed genes.  

Boolean networks have been used in biology to model regulatory networks. Although Boolean networks are a crude simplification of genetic reality where genes are not simple binary switches, there are several cases where they correctly capture the correct pattern of expressed and suppressed genes.  

布尔网络在生物学中已被用于模拟'''<font color="#FF8000">调节网络 regulatory networks </font>'''。虽然布尔网络是对遗传现实的粗略简化，基因不是简单的二进制开关，但在一些情况下，它们正确地捕捉了表达和抑制基因的正确模式。

布尔网络在生物学中已被用于模拟'''<font color="#FF8000">调节网络 Regulatory Networks </font>'''。虽然布尔网络是对遗传现实的粗略简化，基因不是简单的二进制开关，但在一些情况下，它们正确地捕捉了表达和抑制基因的正确模式。

The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s.<ref name=DrosselRbn>{{cite book|last1=Drossel|first1=Barbara|editor1-last=Schuster|editor1-first=Heinz Georg|title=Chapter 3. Random Boolean Networks|date=December 2009|doi=10.1002/9783527626359.ch3|arxiv=0706.3351|series=Reviews of Nonlinear Dynamics and Complexity|publisher=Wiley|pages=69–110|isbn=9783527626359|chapter=Random Boolean Networks}}</ref>

The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s.<ref name=DrosselRbn>{{cite book|last1=Drossel|first1=Barbara|editor1-last=Schuster|editor1-first=Heinz Georg|title=Chapter 3. Random Boolean Networks|date=December 2009|doi=10.1002/9783527626359.ch3|arxiv=0706.3351|series=Reviews of Nonlinear Dynamics and Complexity|publisher=Wiley|pages=69–110|isbn=9783527626359|chapter=Random Boolean Networks}}</ref>

A Boolean network is a particular kind of sequential dynamical system, where time and states are discrete, i.e. both the set of variables and the set of states in the time series each have a bijection onto an integer series. Such systems are like cellular automata on networks, except for the fact that when they are set up each node has a rule that is randomly chosen from all 2}} possible ones with K inputs. With K=2 class 2 behavior tends to dominate. But for K>2, the behavior one sees quickly approaches what is typical for a random mapping in which the network representing the evolution of the 2 states of the N underlying nodes is itself connected essentially randomly.

A Boolean network is a particular kind of sequential dynamical system, where time and states are discrete, i.e. both the set of variables and the set of states in the time series each have a bijection onto an integer series. Such systems are like cellular automata on networks, except for the fact that when they are set up each node has a rule that is randomly chosen from all 2}} possible ones with K inputs. With K=2 class 2 behavior tends to dominate. But for K>2, the behavior one sees quickly approaches what is typical for a random mapping in which the network representing the evolution of the 2 states of the N underlying nodes is itself connected essentially randomly.

布尔网络是一种特殊的顺序动力学系统，其中时间和状态都是离散的，即时间序列中的变量集和状态集都各自有一个偏射到一个整数序列上。这样的系统就像网络上的细胞自动机一样，只是当它们被建立起来时，每个节点都有一个规则，这个规则是从所有''2^k''可能的规则中随机选择的，有''K''个输入。在''K=2''时，两类行为往往占主导地位。但对于''K>2''，人们看到的行为很快就会接近随机映射的典型特征，其中代表''N''个底层节点的''2^k''种状态演化的网络本身基本上是随机连接的。

布尔网络是一种特殊的顺序动力学系统，其中时间和状态都是离散的，即时间序列中的变量集和状态集都各自有一个偏射到一个整数序列上。这样的系统就像网络上的细胞自动机一样，只是当它们被建立起来时，每个节点都有一个规则，这个规则是从所有 ''2^k'' 可能的规则中随机选择的，有 ''K'' 个输入。在 ''K=2'' 时，两类行为往往占主导地位。但对于 ''K>2'' ，人们看到的行为很快就会接近随机映射的典型特征，其中代表 ''N'' 个底层节点的 ''2^k'' 种状态演化的网络本身基本上是随机连接的。

A random Boolean network&nbsp;(RBN) is one that is randomly selected from the set of all possible boolean networks of a particular size, N.  One then can study statistically, how the expected properties of such networks depend on various statistical properties of the ensemble of all possible networks.  For example, one may study how the RBN behavior changes as the average connectivity is changed.

A random Boolean network&nbsp;(RBN) is one that is randomly selected from the set of all possible boolean networks of a particular size, N.  One then can study statistically, how the expected properties of such networks depend on various statistical properties of the ensemble of all possible networks.  For example, one may study how the RBN behavior changes as the average connectivity is changed.