Two kinds of generalized gradient representations for Birkhoffian system in the event space
WANG Jiahang1,2， BAO Siyuan1
1.College of Civil Engineering， Suzhou University of Science and Technology， Suzhou， Jiangsu 215011，China；2.College of Civil and Transportation Engineering， Hehai University， Nanjing 210098，China
Abstract：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.
王嘉航,鲍四元. 事件空间中Birkhoff系统的两类广义梯度表示[J]. 华中师范大学学报(自然科学版), 2020, 54(2): 174-177.
WANG Jiahang,BAO Siyuan. Two kinds of generalized gradient representations for Birkhoffian system in the event space. journal1, 2020, 54(2): 174-177.
2020, Vol. 54 
