2025/11/06 by Michael Robinson, Robinson, Michael, Michael L. Szulczewski +3
Computer Science · Environmental Science · Physics and Astronomy · #18F20 #46M20 #Algebraic Topology (math.AT) #Ecosystem dynamics and resilience #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Origins and Evolution of Life
paper · pdf · doi:10.48550/arxiv.2511.04603
openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from DSEMs to sheaves passes through a formal construction borrowed from electronics called a netlist that specifies how data route through a system. A sheaf can be considered a formal hypothesis about how variables interact, that then specifies how observations can be tested for consistency, how missing data can be inferred, and how uncertainty about the observations can be quantified. Sheaf modeling provides a coherent mathematical framework for studying the interaction of various dynamical subsystems that together determine a larger system.