NOISE-INFLUENCED DYNAMICS OF A VERTICALLY EXCITED PENDULUM

While the effects of noise on a dynamical system are often considered to be detrimental, noise can also have beneficial effects on the response of a system. In this work, the vertically excited pendulum is used as an example to illustrate the beneficial effects of noise. The upright equilibrium position of this system can be stabilized passively with a high-frequency excitation by utilizing the system nonlinearities and a bifurcation. After introducing white Gaussian noise into the pendulum pivot motion, the stability of the system prior to this bifurcation is analyzed. It is shown that white Gaussian noise has the potential to stabilize the unstable equilibrium point. Considering the bi-stable pendulum, a control scheme is introduced which utilizes only noise to switch between the two stable equilibrium points. This system is studied on the basis of an Ito scheme and direct numerical simulations are carried out by using the Euler-Maruyama method, and also with a semi-analytical formulation based on the Fokker-Planck equation. The results of the work can provide a basis to develop noise-utilizing controllers.