Stability of a Variable Coefficient Star-Shaped Network with Distributed Delay  

作　　者：ZHANG Hai-E XU Gen-Qi CHEN Hao LI Min 

机构地区：[1]School of Mathematics,Tianjin University,Tianjin 300350,China [2]Department of Basic Science,Tangshan University,Tangshan 063000,China [3]School of Mechatronical Engineering,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Journal of Systems Science & Complexity》2022年第6期2077-2106,共30页系统科学与复杂性学报（英文版）

基　　金：the National Natural Science Foundation of China under Grant Nos.61773277 and 62073236。

摘　　要：The paper deals with the exponential stability problem of a variable coefficient star-shaped network,whose strings are coupled at a common end in a star-shaped configuration and the common connection of all strings can be moved.Two kinds of media materials with a component of viscous and another simply elastic are distributed on each string.Under suitable hypothesis on the coefficient functionsμj(x)of damping terms and the kernelsηj(s)of distributed delay terms,the well-posedness of the system is obtained by means of resolvent family theory.In addition,the allocation proportion of the two parts and the property of the material character functions are discussed when the starshaped network is exponentially stable.Meanwhile,the sufficient condition of exponential stability is established.Numerical simulations are also included to verify the main results.

关 键 词：Allocation proportion elastic and viscous exponential stability resolvent family starshaped network 

分 类 号：O157.5[理学—数学]