Dynamics of an anharmonic oscillator with a periodic perturbation

We study the features of the stochastic dynamics of a Hamiltonian system with the potential x2n subjected to an external monochromatic perturbation. Three regimes of stochastic diffusion, which differ in the value of the amplitude of the external perturbation, are detected. We demonstrate the possibility of chaotic regimes manifesting themselves in pendulum vibrations of the well of a water-moderated and-cooled nuclear power reactor as an application of the model being investigated. Finally, we propose a method of simple proportional control, which makes it possible to control the chaotic vibrations of the anharmonic oscillator.