Landscape and flux decomposition for exploring global natures of non-equilibrium dynamical systems under intrinsic statistical fluctuations

► We develop a general landscape and flux framework to explore the global physical nature of non-equilibrium dynamical systems under intrinsic fluctuations. Using this method, we explore the global nature of the dynamic system under perturbations, while not only the local properties of the system. ► We found that the underlying potential landscape has a Mexican hat ring valley shape. The driving force of the dynamical systems can be decomposed into three terms: gradient of underlying potential landscape, curl flux, and inhomogeneity of diffusion. The landscape attracts the system down to the oscillation ring while the curl flux on the oscillation ring drives the coherent oscillation. ► We also identified the barrier heights characterizing the landscape topography as a quantitative measure of the global stability of the dynamical system. The high barrier heights guarantee the stability and coherence of the oscillation.