以甘油生物转化生产1,3-丙二醇(简记为1,3-PD)的间歇发酵酶催化过程为背景,研究一类既无法求得解析解、又没有平衡点的非线性动力系统.论述了该类系统关于初始状态的解集的紧性以及对应的线性变分系统基本矩阵解的性质,并证明了非线性动力系统的强稳定性.所做的研究可以为进一步的数值计算提供理论依据. Based on the batch fermentation process of glycerol biotransformation of 1,3-propanediol (abbreviated as 1,3-PD), a kind of nonlinear dynamic system that can neither obtain analytic solution nor equilibrium point is discussed. The compactness of such systems with respect to the solution set of the initial state and the properties of the basic matrix solution of the corresponding linear variational system are also proved and the strong stability of the nonlinear dynamical system is proved.The research can provide the theory for further numerical calculation in accordance with.