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

We develop a theoretical framework for exploring global natures of non-equilibrium dynamical systems under intrinsic statistical fluctuations. We found the underlying driving force can be decomposed into three terms: gradient of potential landscape, curl probability flux, inhomogeneity of diffusion. We studied a limit cycle oscillation model and found that the potential landscape has a Mexican hat close ring valley shape and attracts the system down to the ring while the curl probability flux on the ring drives the coherent oscillation. The barrier heights characterizing the landscape topography provide a quantitative measure for global stability of non-equilibrium dynamical systems.