苏州科技大学学报（自然科学版）2026，Vol.43Issue(2)：30-35,6.DOI:10.12084/j.issn.2096-3289.2026.02.004
自治Birkhoff系统Herglotz方程的组合梯度表示及其解的稳定性
The combined gradient representation and solution stability of Herglotz equations for autonomous Birkhoffian systems
摘要
Abstract
As a class of differential equation systems with favorable properties,gradient systems can be utilized for stability analysis if a mechanical system can be changed into a gradient system.This paper adopts a gradient approach to study the stability of solutions to the Herglotz equations for autonomous Birkhoffian systems.First,the Herglotz equations of the system were established and expressed in contravariant algebraic forms.According to six types of combined gradient systems,the conditions under which the Herglotz equations of the autonomous Birkhoffian system can be transformed into these six types of combined gradient systems were given,and the solutions and their stability were subsequently analyzed.Finally,through six examples,the specific computational process of transforming the Herglotz equations of Birkhoffian systems into six types of combined gradient systems was demonstrated,verifying the validity of the obtained results.关键词
Birkhoff系统/Herglotz方程/组合梯度表示/稳定性Key words
Birkhoffian system/Herglotz equation/combined gradient representation/stability分类
数理科学引用本文复制引用
姚超凡,张毅..自治Birkhoff系统Herglotz方程的组合梯度表示及其解的稳定性[J].苏州科技大学学报（自然科学版）,2026,43(2):30-35,6.基金项目
国家自然科学基金面上项目(12272248) （12272248）
