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

Shirui Bian; Ruisong Zhou; Wei Lin; Chunhe Li

doi:10.1016/j.xpro.2025.103922

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

STAR Protoc. 2025 Jun 27;6(3):103922. doi: 10.1016/j.xpro.2025.103922. Online ahead of print.

Authors

Shirui Bian¹, Ruisong Zhou², Wei Lin³, Chunhe Li⁴

Affiliations

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China. Electronic address: srbian23@m.fudan.edu.cn.
² School of Mathematical Sciences, Fudan University, Shanghai 200433, China.
³ School of Mathematical Sciences, Fudan University, Shanghai 200433, China; Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200438, China; Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China; State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institute of Brain Science, Fudan University, Shanghai 200032, China. Electronic address: wlin@fudan.edu.cn.
⁴ School of Mathematical Sciences, Fudan University, Shanghai 200433, China; Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200438, China; Shanghai Key Laboratory for Contemporary Applied Mathematics and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China. Electronic address: chunheli@fudan.edu.cn.

PMID: 40580473
DOI: 10.1016/j.xpro.2025.103922

Abstract

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.

Keywords: Biophysics; Computer sciences; Physics.