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多重稳定性是许多分子生物模型重要的动力学行为,它在分析细胞分裂和生长现象中起到关键性的作用。为了了解细胞内的复杂的调节网络的动力学行为,将其数学模型进行单调分解为若干个单调控制系统的互联。对具有惟一定义的稳定状态响应的单调控制系统,引入了具有保持局部稳定性质的简化系统,根据简化系统的平衡点与原来单调控制系统的平衡点之间存在的一一对应的映射关系,可推知单调控制系统的平衡点的位置及其稳定性。进而通过确定单调控制系统的平衡点的位置及平衡点的稳定性,来确定整个互联单调控制系统的平衡点的位置及平衡点的稳定性。由于简化系统降低了原来生物系统模型的维数,这为分析复杂生物系统的稳定性提供了一种可行的途径。
Multiple stability is an important kinetic behavior of many molecular biological models and plays a key role in the analysis of cell division and growth phenomena. In order to understand the dynamics of complex regulatory networks in cells, the mathematic model is monotonely decomposed into interconnections of several monotonic control systems. For a monotonic control system with a uniquely defined steady state response, a simplified system with locally stable properties is introduced. According to the one-to-one correspondence between the equilibrium point of the simplified system and the equilibrium point of the original monotonic control system, Deduce the position and stability of the equilibrium point of the monotonic control system. Then the position of the equilibrium point and the stability of the equilibrium point of the monolithic interconnected monotonic control system are determined by determining the position of the equilibrium point and the stability of the equilibrium point of the monotonic control system. Because simplifying the system reduces the dimensions of the original biological system model, this provides a viable approach for analyzing the stability of complex biological systems.