复杂布尔网络的同步-应用数学专业论文.docxVIP

复杂布尔网络的同步 复杂布尔网络的同步 SYNCHRONIZATION OF COMPLEX BOOLEAN NETWORK ABSTRACT In recent years，boolean networks and synchronization are gradually applied to large-scale gene regulatory network analysis. The advantage is simple and clear. In addition, in the life sciences, financial science, and other complex systems typically have played an important role in the study. This article studies synchronization of traditional boolean networks and probabilistic boolean network and random coupling boolean network. For traditional boolean network, graphic method and truth table method and logical operators were used to analyze their network synchronization. For probabilistic boolean network, a probability matrix is proposed. P(t) = MAt .The purpose is calculate the probability of Selecting an initial state into a certain state in time t. Where A is the probability transformation matrix, M is the initial state probability matrix. And for all initial state, a probabilistic boolean network into a state in time t , the total probability  p i ( t ) =  2 ∑ k = 1  p ( t ) , Where  p(t ) ki  is the probability of a probabilistic boolean network in the time t from the initial state k into a state j ,to facilitate research probabilistic boolean network synchronization. And a probabilistic Boolean network to be broken down into traditional boolean network, and use methods similar to the above to analyze a traditional boolean network. random coupling boolean network, if the ratio of node reaches a certain state is 1, then to achieve synchronization. In addition, constructed the coupling of two random Boolean networks, all corresponding node tends to same, then lim || y (t) ? x (t) ||= 0 Or lim | p 1 (t ) ? p 2 |= 0， t ?∞ i i t ? ∞ where pi (t) is ratio of i -network in a particular state ,the two Boolean network synchronization. KEY WORDS: boolean network, complex network synchronization, random boolean networks, semi-tensor prod ii 原创性声明 本人郑重声明 :所呈交的学位论文 ，是本人在导师指导下，