CLC number: O316

Gradientization of Herglotz-Type Equations and Stability of Their Solutions

Herglotz型方程组的梯度化与解的稳定性

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu, China

Received: 10 November 2024

Abstract

The stability of solutions of Herglotz-type equations for non-conservative systems is studied by converting them into gradient systems. Firstly, Herglotz-type equations for non-conservative systems are given and expressed in contravariant algebraic form. Secondly, four kinds of basic gradient systems are introduced. Thirdly, the conditions for transforming Herglotz-type equations of non-conservative systems into basic gradient systems are given. Then the solution of Herglotz-type equations and its equilibrium stability are analyzed. Finally, four examples are presented to illustrate the calculation process in detail for each case. The results show that the gradient method is effective.

摘要

通过将非保守系统的Herglotz型方程组化为梯度系统, 研究它们的解的稳定性。首先, 给出非保守系统的Herglotz型方程组, 并以逆变代数形式表示。其次, 介绍四类基本梯度系统。第三, 给出非保守系统Herglotz型方程组化为基本梯度系统的条件。然后分析Herglotz型方程组的解与平衡稳定性。最后, 给出四个实例, 详细演绎每种情况下的计算过程。结果表明, 该梯度化方法是有效的。