Quantifying energy landscape of high-dimensional oscillatory systems by diffusion decomposition

High-dimensional networks producing oscillatory dynamics are ubiquitous in biological systems. Unravelling the mechanism of oscillatory dynamics in biological networks with stochastic perturbations becomes paramountly significant. Although the classical energy landscape theory provides a tool to study this problem in multistable systems and explain cellular functions, it remains challenging to quantify the landscape for high-dimensional oscillatory systems accurately. Here we propose an approach called the diffusion decomposition of Gaussian approximation (DDGA). We demonstrate the efficacy of the DDGA in quantifying the energy landscape of oscillatory systems and corresponding stochastic dynamics, in comparison with existing approaches. By further applying the DDGA to high-dimensional biological networks, we are able to uncover more intricate biological mechanisms efficiently, which deepens our understanding of cellular functions.