2023/11/27 by Lucia S. Layritz, Layritz, Lucia S., Ilya Pavlyukevich +5
Decision Sciences · Economics, Econometrics and Finance · Environmental Science · #Complex Systems and Decision Making #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #Ecosystem dynamics and resilience #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2311.16350
openalex publication_date 2023/11/27 · openalex created_date 2023/11/30 · openalex updated_date 2026/07/28
Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the identification of potential rapid, non-linear change or tipping points. However, the reliability of these early warning signs relies on a number of key mathematical assumptions, most notably the presence of Gaussian noise. We here show that for systems driven by non-Gaussian, α-stable noise, the classical early warning signs of rising variance and autocorrelation are not supported by mathematical theory and their use poses the danger of spurious, false-positive results. To address this, we provide a generalized approach by introduce the scaling factor γX as an alternative early warning sign. We show that in the case of the Ornstein-Uhlenbeck process, there exists a direct inverse relationship between γX and the bifurcation parameter, telling us that γX will increase as we approach the bifurcation. Our numerical simulations confirm theoretical results and show that our findings generalize well to non-linear, non-equilibrium systems. We thus provide a generalized, robust and applicable statistical early warning sign for systems driven by Gaussian and non-Gaussian α-stable noise.