38
个编辑
更改
跳到导航
跳到搜索
第327行：
第327行： − − − − − <math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math> − − − − − <math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math> − − − + − − − −
无编辑摘要
一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔振子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)
一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔振子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)
:<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>
:<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>
:<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>
:<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>
where, for convenience, the rate constants have been set to 1.
where, for convenience, the rate constants have been set to 1.
其中，为了方便起见，速率常数被设置为1。
其中，为了方便起见，速率常数被设置为1。
<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>
<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>
[[File:080205 Brusselator picture.jpg|thumb|right|350px|The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle]]. For B<1+A the system is stable and approaches a [[Fixed point (mathematics)|fixed point]].|链接=Special:FilePath/080205_Brusselator_picture.jpg]]
[[File:080205 Brusselator picture.jpg|thumb|right|350px|The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle]]. For B<1+A the system is stable and approaches a [[Fixed point (mathematics)|fixed point]].|链接=Special:FilePath/080205_Brusselator_picture.jpg]]