特征多项式理论在布尔控制网络中的应用

The Application of Characteristic Polynomial Theory in Boolean Control Network

摘要: 首先，本文介绍了布尔控制网络的基本概念。然后，我们利用特征多项式方法研究布尔控制网络的动力学性质，包括极限环、吸引子与暂态，并以哺乳动物细胞周期调节网络为例进行说明。其次，本文利用一个布尔逻辑方程模拟网络演化过程中的状态突变，研究了单个节点扰动对布尔控制网络动力学性质的影响。接着，本文从特征多项式的角度研究了主从动布尔控制网络的动力学性质，得到其同步关系。该方法可以简便有效地得到布尔控制网络的动力学性质。

Abstract: First, this paper introduces the basic concepts of Boolean Control Networks. Second, we use the method of characteristic polynomial to study the dynamics of the Boolean Control Network, including limit cycles, attractors and transients, and use a mammalian cell cycle regulation network as an example. Next, this paper uses a Boolean logical expression to simulate the state mutation in the network evolution process, and studies the influence of individual node disturbance on the dynamics of the Boolean control network. Then, from the perspective of characteristic polynomials, this paper studies the dynamic properties of the master-slave Boolean control network and obtains its synchronization relationship. This method can easily and effectively get the dynamics of Boolean control network.