Data-driven stability analysis of complex systems with higher-order interactions

Abstract Stability analysis of complex dynamical systems is a fundamental challenge across many disciplines, with implications for a wide range of systems, from ecosystems, to organs in biological systems, such as the heart and brain. We present a data-driven method for assessing the stability of high-dimensional systems by constructing effective weighted adjacency matrices near empirically identified fixed points. Extending beyond pairwise interactions, we quantify higher-order interactions that introduce nonlinear feedback loops, coupling effects, and emergent fixed points, significantly enriching the dynamical landscape of such systems. The approach is demonstrated and validated by analyzing both low- and high-dimensional nonlinear systems featuring tipping elements, demonstrating its robustness and accuracy, as well as its application to the stability of the Nordic Power Grid, hence underscoring its potential for addressing stability challenges in complex real-world dynamical systems.