Existence and structure analysis of attractors for new delayed Kirchhoff-type suspension bridge equations under stochastic perturbations with applications

Abstract

This paper investigates the existence and structure of global attractors for a new class of delayed Kirchhoff-type suspension bridge equations under stochastic perturbations. Through the application of infinite-dimensional dynamical system techniques, we establish the well-posedness of the problem and the existence of a global attractor in a bounded absorbing set. The system's long-term stability despite the presence of random external perturbations is proven through the asymptotic smoothness of the governing semigroup. Moreover, we examine the dynamical and topological properties of the attractor, and prove that it possesses finite fractal dimension under subcritical conditions. In addition, we provide numerical simulations and applications showing how our results model the vibrations of suspension bridges under stochastic environmental forces, such as wind and traffic loads. Also, we validate our theoretical obtained results through computational analysis. This work supports suspension bridge optimization, with future focus on stability in stochastic environments, advanced control, and numerical efficiency.