Résumé
In this paper, we first consider second order dynamical systems of the forme , and , where is a cocoercive operator defined on a Hilbert space , and is a damping coefficient. We investigate stability and sensitivity when external parameters are involved at the level of both of the associated operator and the initial values. The obtained result is thereafter discussed with respect to several particular interesting cases regarding parametric heavy ball with friction dynamic, second order dynamics associated to fixed point and the dynamics governed by the Yosida approximation. Further quantitative stability results are also established when the perturbations are measured in terms of metrics between operators. Secondly, we investigate both Hölder and Lyapunov stability under parametric perturbations for perturbed inertial gradient-like dynamics with Hessian-driven damping, () for short, which we apply to derive an interesting quantitative stability result for parametric minimization problems by relying on the asymptotic analysis presented in Alvarez et al [10]. In the subsequent step of the work, we present a new quantitative stability result under a partial variation of the data of the problem by involving exact and/or approximate fixed points for which we apply Lim's Lemma either in its exact format or in its very recent approximate version, wherein we underline that a qualitative convergence of approximate solutions to the exact solution permits us to find again the exact stability estimate, which is a coherent conclusion with the main purpose of the paper. We end the present contribution by an outline of some perspectives.