Generalized Gradient Method for the Stability of Solutions to Herglotz-Type Equations for Non-Autonomous Non-Conservative Systems

The stability of solutions of Herglotz-type equations for non-autonomous non-conservative systems is studied by means of generalized gradient method. Firstly, Herglotz-type equations for non-conservative systems are given and expressed as contravariant algebraic form. Secondly, two classes of generalized gradient systems are introduced. Thirdly, the conditions for the transformation of Herglotz-type equations into generalized gradient systems are given, and the solutions of Herglotz-type equations and the stability of the solutions are analyzed. Finally, for each case discussed in this paper, the calculation process is demonstrated in detail to show that the method is effective.