Combined Gradient Representations for Generalized Birkhoffian Systems in Event Space and Its Stability Analysis

doi:10.16356/j.1005-1120.2021.06.007

Transactions of Nanjing University of Aeronautics & Astronautics

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Combined Gradient Representations for Generalized Birkhoffian Systems in Event Space and Its Stability Analysis

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Abstract:

The combined gradient representations for generalized Birkhoffian systems in event space are studied. Firstly， the definitions of six kinds of combined gradient systems and corresponding differential equations are given. Secondly， the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally， the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.

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This work was supported by the National Natural Science Foundation of China （No.11972241）， the Natural Science Foundation of Jiangsu Province （No.BK20191454）， and the Scientific Research Foundation of Suzhou University of Science and Technology （No.XKZ2017005）. In addition， we would like to thank professor ZHANG Yi for his helpful suggestions in the research of this paper.

Clc Number:

O316