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添加18字节 、 2020年10月30日 (五) 18:32
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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
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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
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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
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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,&nbsp;y,&nbsp;z) = (1&nbsp;+&nbsp;x)(1&nbsp;+&nbsp;y)(1&nbsp;+&nbsp;z) with arithmetic modulo 2 for all vertex functions. Using the update sequence (1,2,3,4) then the system state (0,&nbsp;1,&nbsp;0,&nbsp;0) is mapped to (0,&nbsp;0,&nbsp;1,&nbsp;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,&nbsp;y,&nbsp;z) = (1&nbsp;+&nbsp;x)(1&nbsp;+&nbsp;y)(1&nbsp;+&nbsp;z) with arithmetic modulo 2 for all vertex functions. Using the update sequence (1,2,3,4) then the system state (0,&nbsp;1,&nbsp;0,&nbsp;0) is mapped to (0,&nbsp;0,&nbsp;1,&nbsp;0). All the system state transitions for this sequential dynamical system are shown in the phase space below.
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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。
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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。
     
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