Stochastic nonlinear dynamic characteristics and safe basin of Li-doped graphene impacted by hydrogen atoms

In this article, stochastic nonlinear dynamic characteristics and safe basin of a Li-doped graphene impacted by hydrogen atoms are studied. The interaction of hydrogen atoms to a graphene is regarded as Gauss white noise excitation. The nonlinear dynamic model of a Li-doped graphene impacted by hydrogen atoms is developed, in which the effect of Li atoms on graphene's stiffness is considered. The local and global stability of the system are analyzed, and the system's safe basin is obtained. The reliability function of the system is solved, and the probability of the first-passage time is determined. Theoretical analysis and numerical simulation show that the safe basin's boundary has fractal characteristics, which means chaos induced by noise; the safe basin's area decreases when the noise's intensity increases; the inhomogeneity of the graphene's stiffness can affect the system's safe basin, which decides the graphene's actual hydrogen storage capacity. Finally, the phenomena of the graphene's stiffness changing with the temperature are explained.