Nonlinear dynamic characteristics and bifurcation analysis of Al-doped graphene impacted by hydrogen atoms

In this paper, the nonlinear dynamic characteristics and bifurcation of Al-doped graphene are studied. The nonlinear dynamic model of Al-doped graphene impacted by hydrogen atoms is developed where the nonlocal effect of a graphene is considered. The natural frequency of the system is obtained, the system's drift coefficient and diffusion coefficient are verified, and the stationary probability density function of the system's dynamic response is given. The condition of stochastic bifurcation is determined, and the fractal boundary of the safe basin is provided. Finally, the reliability function of the system is solved, and the probability density of the first-passage time is determined. Theoretical analysis and numerical simulation show that stochastic bifurcation occurs in the variation of parameters; the area of safe basin decreases when the intensity of the atom's impact increases. The results of this paper are helpful for the application of Al-doped graphene in hydrogen storage.