更改

|2002

|2002

|与系统大小成线性关系,

|与系统大小成线性关系

|<math>\langle\nu\rangle \sim N</math>

|<math>\langle\nu\rangle \sim N</math>

|2003

|2003

|快于线性关系,

|长度增长速度大于线性关系

|<math>\langle\nu\rangle > N^x</math>  <math>x > 1</math>

|<math>\langle\nu\rangle > N^x</math>  <math>x > 1</math>

|2003

|2003

|超多项式增长,

|长度呈超多项式增长

|<math>\langle\nu\rangle > N^x \forall x</math>

|<math>\langle\nu\rangle > N^x \forall x</math>

|}

|}

==Stability==

==稳定性==

In dynamical systems theory, the structure and length of the attractors of a network corresponds to the dynamic phase of the network. The stability of Boolean networks depends on the connections of their nodes. A Boolean network can exhibit stable, critical or chaotic behavior. This phenomenon is governed by a critical value of the average number of connections of nodes (<math>K_{c}</math>), and can be characterized by the Hamming distance as distance measure. In the unstable regime, the distance between two initially close states on average grows exponentially in time, while in the stable regime it decreases exponentially. In this, with "initially close states" one means that the Hamming distance is small compared with the number of nodes (<math>N</math>) in the network.

在动力系统理论中，网络的结构和吸引子的长度与网络所处的动态阶段相对应。布尔网络的'''<font color="#FF8000">稳定性 Stability</font>'''取决于其节点的连接。布尔网络可以表现出稳定、临界或'''<font color="#FF8000">混沌chaos</font>'''的行为。这种现象受节点平均连接数的临界值（<math>K_{c}</math>）支配，可以用'''<font color="#FF8000">汉明距离Hamming distance</font>'''作为距离度量。在不稳定机制下，随着时间增长，两个初始接近状态之间的平均距离呈指数级增长，而在稳定机制下则呈指数级减小。在这种情况下， "最初接近的状态 "意味着状态间的汉明距离与网络中的节点数（<math>N</math>）相比是很小的。

在动力系统理论中，网络的结构和吸引子的长度对应于网络的动态阶段。布尔网络的稳定性取决于其节点的连接。布尔网络可以表现出稳定、临界或混乱的行为。这种现象受节点平均连接数的临界值（<math>K_{c}</math>）支配，可以用汉明距离作为距离度量。在非稳定体制下，两个初始接近状态之间的平均距离在时间上呈指数级增长，而在稳定体制下则呈指数级减小。在这其中，用 "最初接近的状态 "意味着汉明距离与网络中的节点数（<math>N</math>）相比是很小的。

对于'''<font color="#FF8000">N-K模型 N-K-model<ref>{{cite journal |last=Kauffman |first=S. A. |date=1969 |title=Metabolic stability and epigenesis in randomly constructed genetic nets |journal=Journal of Theoretical Biology |volume=22 |issue=3 |pages=437–467 |doi=10.1016/0022-5193(69)90015-0|pmid=5803332 }}</ref> </font>'''，如果 <math>K<K_{c}</math> ，网络是稳定的；如果 <math>K=K_{c}</math> ，网络是处于临界状态的；如果 <math>K>K_{c}</math> ，网络是不稳定的。

 

 

For '''N-K-model'''<ref>{{cite journal |last=Kauffman |first=S. A. |date=1969 |title=Metabolic stability and epigenesis in randomly constructed genetic nets |journal=Journal of Theoretical Biology |volume=22 |issue=3 |pages=437–467 |doi=10.1016/0022-5193(69)90015-0|pmid=5803332 }}</ref> the network is stable if <math>K<K_{c}</math>, critical if <math>K=K_{c}</math>, and unstable if <math>K>K_{c}</math>.

 

 

对于N-K模型，如果 <math>K<K_{c}</math> ，网络是稳定的；如果 <math>K=K_{c}</math> ，网络是临界的；如果 <math>K>K_{c}</math> ，网络是不稳定的。

The state of a given node <math> n_{i} </math> is updated according to its [[truth table]], whose outputs are randomly populated. <math> p_{i} </math> denotes the probability of assigning an off output to a given series of input signals.

The state of a given node <math> n_{i} </math> is updated according to its [[truth table]], whose outputs are randomly populated. <math> p_{i} </math> denotes the probability of assigning an off output to a given series of input signals.

The state of a given node <math> n_{i} </math> is updated according to its truth table, whose outputs are randomly populated. <math> p_{i} </math> denotes the probability of assigning an off output to a given series of input signals.

The state of a given node <math> n_{i} </math> is updated according to its truth table, whose outputs are randomly populated. <math> p_{i} </math> denotes the probability of assigning an off output to a given series of input signals.给给定的一系列输入信号分配一个off输出的概率。

一个给定节点的状态 <math>n_{i}</math> 根据其真值表进行更新，真值表的输出是随机填充的。<math>p_{i}</math> 表示将关闭输出分配给给定系列输入信号的概率。

一个给定节点的状态 <math>n_{i}</math> 根据其'''<font color="#FF8000">真值表truth table</font>'''进行更新，真值表的输出是随机填充的。<math>p_{i}</math> 表示对给定的一系列输入信号分配一个关闭输出信号指令的概率。将关闭输出分配给给定系列输入信号的概率。