本文的重要研究成果是發現隨機布爾網路於臨界相位且k愈大時的網路行為並不如前人所認為會發生混沌的現象，反而是傾向凍住的行為，即k愈大時，吸引子長度及數目分布愈短且愈少，也就是說，在大k且臨界相位時，元素狀態大多分布在流域裡。而且本文數值模擬發現，當10≤N≤350，2≤k≤6且臨界相位情形時(1)有關連元素數目與元素數目N之關係為N_RE∝N^(4/5)；穩定核心數目和元素數目N之關係成正比。(2)當N固定350，2≤k≤6時，吸引子長度分布呈現類似Poisson型態，但吸引子數目的分布卻呈現類似power-law型態。 

The most important conclusion of our thesis is that we found that Random Boolean networks on critical phase will not have appearance of chaos but it will have appearance of frozen when k is a high number. In other words, the distributions of attractor length and number will be short and few when k is higher. That is to say, when Random Boolean network is on critical phase and k is higher, most of states of elements will distribute in basin. Our numerical simulation finds that the two conclusions will follow the two statements below when Random Boolean network is on critical phase and 10≤N≤350，2≤k≤6. (1) The relation which is between relevant elements,“N_RE”, and the number of elements,“N”,is N_RE∝N^(4/5).Stable cores and the number of elements,“N”, are in direct proportion. (2) When we have 2≤k≤6 for N=350, the distribution of attractor length will be similar to Poisson distribution, but attractor numbers will be similar to power-law distribution.

中文摘要 …………………………………………………… i
英文摘要 …………………………………………………… ii
誌謝辭 …………………………………………………… iii
目錄 …………………………………………………… iv
圖目錄 …………………………………………………… vi
第一章 緒論……………………………………………… 1
1-1 問題背景………………………………………… 1
1-2 研究動機與目的………………………………… 2
1-2-1研究動機………………………………………… 2
1-2-2研究目的………………………………………… 3
1-3 名詞釋義………………………………………… 3
1-4 論文之主要架構………………………………… 5
第二章 文獻探討………………………………………… 5
2-1 隨機布爾網路的拓樸構形與相位……………… 6
2-2 隨機布爾網路的吸引子數目與長度…………… 8
2-3 隨機布爾網路的穩定核心……………………… 13
2-4 隨機布爾網路的有關連元素…………………… 14
2-5 近來的研究方向………………………………… 19
第三章 研究方法與步驟………………………………… 20
第四章 結果與討論……………………………………… 21
4-1 平均循環長度、平均循環數目、平均穩定核心
數目及平均有關連元素與元素數目N的函數關
係………………………………………………… 22
4-2 循環長度及循環數目在N=350，k=2~6情形的
分布圖…………………………………………… 29
4-3 全部模擬的網路之討論………………………… 43
第五章 結果與建議……………………………………… 51
5-1 結論……………………………………………… 51
5-2 未來展望………………………………………… 54
參考文獻 …………………………………………………… 57

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