Protocol to quantify energy landscape of high-dimensional oscillatory systems using diffusion decomposition

Here, we present a numerical framework to quantify the energy landscape of high-dimensional stochastic oscillatory systems, based on the diffusion decomposition of Gaussian approximation (DDGA). We describe steps for downloading codes, setting the oscillatory dynamics, and calculating the one-dimensional pre-solution along the limit cycle and the covariance matrix on normal planes. We then detail procedures for quantifying the global landscape through the DDGA. For complete details on the use and execution of this protocol, please refer to Bian et al.¹.