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→Sequential dynamical systems (SDS) 序列动力系统
If the vertex functions are applied asynchronously in the sequence specified by a word w = (w<sub>1</sub>, w<sub>2</sub>, ... , w<sub>m</sub>) or permutation <math>\pi</math> = ( <math>\pi_1</math>, <math>\pi_2,\dots,\pi_n</math>) of v[Y] one obtains the class of Sequential dynamical systems (SDS). In this case it is convenient to introduce the Y-local maps F<sub>i</sub> constructed from the vertex functions by
If the vertex functions are applied asynchronously in the sequence specified by a word w = (w<sub>1</sub>, w<sub>2</sub>, ... , w<sub>m</sub>) or permutation <math>\pi</math> = ( <math>\pi_1</math>, <math>\pi_2,\dots,\pi_n</math>) of v[Y] one obtains the class of Sequential dynamical systems (SDS). In this case it is convenient to introduce the Y-local maps F<sub>i</sub> constructed from the vertex functions by
如果顶点函数按照 v [ y ]中 w (w 子1 / sub，w 子2 / sub，... ，w 子 m / sub)或置换数学 pi / math (math pi 1 / math，math pi 2， dots， pi n / math)指定的序列异步应用，则得到'''<font color="#ff8000"> Sequential dynamical systems (SDS) 序列动力系统</font>''的类。在这种情况下，可以方便地引入由顶点函数构造的 y 局部映射 f 子 i / 子
如果顶点函数按照 v [ y ]中 w (w 子1 / sub，w 子2 / sub，... ，w 子 m / sub)或置换数学 pi / math (math pi 1 / math，math pi 2， dots， pi n / math)指定的序列异步应用，那么我们可以得到'''<font color="#ff8000"> Sequential dynamical systems (SDS) 序列动力系统</font>''的类。在这种情况下，可以方便地引入由顶点函数构造的 y 局部映射 f 子 i / 子
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的这个顺序动力系统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。