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→Sequential dynamical systems (SDS) 序列动力系统
If the update sequence is a permutation one frequently speaks of a permutation SDS to emphasize this point.
If the update sequence is a permutation one frequently speaks of a permutation SDS to emphasize this point.
如果新序列是置换序列，那么我们就经常使用置换 '''<font color="#ff8000"> SDS</font>''' map ''F'' = [''F<sub>Y</sub>'' 以强调这一点。
Example: Let Y be the circle graph on vertices {1,2,3,4} with edges {1,2}, {2,3}, {3,4} and {1,4}, denoted Circ<sub>4</sub>. Let K={0,1} be the state space for each vertex and use the function nor<sub>3</sub> : K<sup>3</sup> → K defined by nor<sub>3</sub>(x, y, z) = (1 + x)(1 + y)(1 + z) with arithmetic modulo 2 for all vertex functions. Using the update sequence (1,2,3,4) then the system state (0, 1, 0, 0) is mapped to (0, 0, 1, 0). All the system state transitions for this sequential dynamical system are shown in the phase space below.
Example: Let Y be the circle graph on vertices {1,2,3,4} with edges {1,2}, {2,3}, {3,4} and {1,4}, denoted Circ<sub>4</sub>. Let K={0,1} be the state space for each vertex and use the function nor<sub>3</sub> : K<sup>3</sup> → K defined by nor<sub>3</sub>(x, y, z) = (1 + x)(1 + y)(1 + z) with arithmetic modulo 2 for all vertex functions. Using the update sequence (1,2,3,4) then the system state (0, 1, 0, 0) is mapped to (0, 0, 1, 0). All the system state transitions for this sequential dynamical system are shown in the phase space below.
例如: 设 y 是顶点{1,2,3,4}上的圆图，边{1,2} ，{2,3} ，{3,4}和{1,4} ，表示 Circ 子4 / 子。设 k {0,1}为每个顶点的状态空间，对所有顶点函数使用 nor 子3 / sub: k sup 3 / sup → k，该函数由 nor 子3 / sub (x，y，z)(1 + x)(1 + y)(1 + z)定义，算术模为2。使用更新序列(1,2,3,4) ，然后将系统状态(0,1,0,0)映射到(0,0,1,0)。所有的系统状态，转换下这个动力系统依次显示在下面的相空间。
例如: 设 y 是顶点{1,2,3,4}上的圆图，边{1,2} ，{2,3} ，{3,4}和{1,4} ，表示 Circ 子4 / 子。设 k {0,1}为每个顶点的状态空间，对所有顶点函数使用 nor 子3 / sub: k sup 3 / sup → k，该函数由 nor 子3 / sub (x，y，z)(1 + x)(1 + y)(1 + z)定义，算术模为2。使用新序列(1,2,3,4) ，然后将系统状态(0,1,0,0)映射到(0,0,1,0)。在所有系统状态转换下，这个动力系统依次显示在下面的相空间。