事件空间中Birkhoff系统的两类广义梯度表示  

Two kinds of generalized gradient representations for Birkhoffian system in the event space

作　　者：王嘉航[1,2] 鲍四元[1] WANG Jiahang;BAO Siyuan(College of Civil Engineering, Suzhou University of Science and Technology, Suzhou, Jiangsu 215011,China;College of Civil and Transportation Engineering, Hehai University, Nanjing 210098,China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011 [2]河海大学土木与交通学院,南京210098

出　　处：《华中师范大学学报（自然科学版）》2020年第2期174-177,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(10972151,11272227);苏州科技大学科研基金项目(XKZ2017005).

摘　　要：研究事件空间中Birkhoff系统的广义斜梯度系统和具有对称负定矩阵的广义梯度系统表示.首先,给出了两类广义梯度系统的定义和微分方程,讨论了两类梯度系统与动力学系统稳定性的关系.其次,给出了事件空间中Birkhoff系统成为两类广义梯度系统的条件,最后,利用广义梯度的性质来研究事件空间中Birkhoff系统解的稳定性问题.算例表明在事件空间中对Birkhoff系统利用梯度化方法研究稳定性问题的有效性.Generalized gradient system representations for Birkhoffian systems in the event space were studied,including two kinds of generalized gradient system,i.e.,the skew generalized gradient system and the generalized gradient system with symmetric negative definite matrix.First,the definitions and differential equations of two kinds of generalized gradient systems were given,and the relations of stability between these two kinds of generalized gradient systems and the dynamical systems were studied.Second,the conditions which Birkhoffian systems become generalized gradient systems in the event space were obtained.Finally,the characteristic of the generalized gradient systems were used to study stability of the Birkhoffian systems in the event space.Examples were given to illustrate the application of the method.

关 键 词：BIRKHOFF系统 事件空间 广义梯度系统 

分 类 号：O316[理学—一般力学与力学基础]