2024/12/21 by Yan Luo, Luo, Yan, Kaicheng Sheng +1
Earth and Planetary Sciences · #Aquatic and Environmental Studies #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2412.16639
openalex publication_date 2024/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these stochastic vibrations can be simplified with ergodicity. We give a complete description of the bifurcations of phase portraits of the averaged Hamiltonian system. The bifurcation curves of the stochastic perturbed Hamiltonian system are shown numerically. Estimations between the averaged system and the exact system are calculated. The correspondence of the averaged system to the exact system is explained through the Poincaré return map. Studying the averaged Hamiltonian system provided important information for the exact stochastic perturbed Hamiltonian system.