  The energy landscape theory finds its both extensive and intensive
application in studying stochastic dynamics of physical and biological systems.
Although the weighted summation of the Gaussian approximation (WSGA) approach
has been proposed for quantifying the energy landscape in multistable systems
by solving the diffusion equation approximately from moment equations, we are
still lacking an accurate approach for quantifying the energy landscape of the
periodic oscillatory systems. To address this challenge, we propose an
approach, called the diffusion decomposition of the Gaussian approximation
(DDGA). Using typical oscillatory systems as examples, we demonstrate the
efficacy of the proposed DDGA in quantifying the energy landscape of
oscillatory systems and corresponding stochastic dynamics, in comparison with
existing approaches. By further applying the DDGA to a high-dimensional cell
cycle network, we are able to uncover more intricate biological mechanisms in
cell cycle, which cannot be discerned using previously developed approaches.
