一簇微生物间歇发酵酶催化非线性动力系统强稳定性  

Strong stability of a family enzyme-catalyzed nonlinear dynamic system in microbial batch fermentation

作　　者：柳扬 杨琦[1] 冯恩民 修志龙[3] LIU Yang;YANG Qi;FENG Enmin;XIU Zhilong(School of Mathematical Science,Dalian University of Technology,Dalian 116024,China;College of Information Engineering,Dalian University,Dalian 116622,China;School of Bioengineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]大连大学信息工程学院,辽宁大连116622 [3]大连理工大学生物工程学院,辽宁大连116024

出　　处：《大连理工大学学报》2019年第6期656-662,共7页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(61712121)

摘　　要：针对分段线性连续函数各参量的微生物间歇发酵酶催化非线性动力系统中状态变量及其变化速率的充分光滑性以及辨识参量的分段线性等特征,应用比较原理证明此类非线性动力系统及子动力系统解对应的线性变分系统的基本矩阵解的有界性.提出没有平衡点的非线性动力系统解关于初始点及一列解点上扰动后的强稳定性定义.在适当条件下证明了一簇非线性动力系统NLDS(u(g,t))的强稳定性.In a microbial batch fermentation enzyme-catalyzed nonlinear dynamic system,due to the sufficient smoothness of state variables and rates in a piecewise linear continuous function and the piecewise linearity of identification parameters,the comparison principle is used to prove the boundedness of the fundamental matrix solutions of the linear variational systems corresponded by the nonlinear dynamic system and sub dynamic system solution.The definition of the strong stability of solutions of nonlinear dynamic systems without equilibrium points disturbed on initial point and a serial solution points is proposed.In perfect condition,the strong stability of a family nonlinear dynamic system NLDS(u(g,t))is proved.

关 键 词：非线性动力系统 线性变分系统 基本矩阵解 强稳定性 

分 类 号：O175.14[理学—数学]