20.500.12556/DKUM-97761 A discrete-time benchmark for assessing critical slowing down indicators We introduce a low-dimensional, discrete-time benchmark for evaluating critical slowing down indicators and early-warning signals in the presence of complex dynamics. Starting from a map-based attention-deficit-disorder model, we add a bias offset to obtain a modified system with a controllable, hysteresis-like coexistence band. Within this band, forward and backward parameter sweeps follow distinct branches, and abrupt switching can occur alongside periodic windows and chaotic regimes. We characterize the dynamics using state-space portraits, bifurcation diagrams, and Lyapunov exponents. We then evaluate four metric-based indicators - lag-1 autocorrelation, variance, skewness, and kurtosis - using a period-aware computation designed for regimes beyond period-one. We find that variance exhibits the most consistent warning trend near the coexistence boundaries, whereas autocorrelation is more susceptible to spurious spikes. Higher-order moments are generally less reliable, particularly in intermittently chaotic regions. Overall, the benchmark is computationally efficient and provides a practical testbed for stress-testing early-warning methods and for quantifying sensitivity to analysis choices. early warning signal critical slowing down indicators hysteresis chaos critical phase transition zgodnji opozorilni signal indikatorji kritičnega upočasnjevanja histereza kaos kritični fazni prehod true false true Angleški jezik Slovenski jezik Znanstveno delo 2026-04-10 10:39:09 2026-04-10 10:39:09 2026-04-11 03:07:34 0000-00-00 00:00:00 2026 0 0 14 str. št. 1, št. članka 015013 Letn. 7 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 2026-03-17 2026-03-31 53.01:517.938 274802179 10.1088/2632-072X/ae5384 2632-072X RAZ_Jafari_Sajad_2026.pdf RAZ_Jafari_Sajad_2026.pdf 1 B8537679D834773DAD9743D5A0F8612A d362fd952e9a230d44ed2cd04ba180db64dd6076a390e8a5659b0ffd7059bde7 e1d19686-34b8-11f1-92c6-00155d0001a1 https://dk.um.si/Dokument.php?lang=slv&id=205179 https://iopscience.iop.org/article/10.1088/2632-072X/ae5384 1 a735c462-34b8-11f1-92c6-00155d0001a1 https://dk.um.si/Dokument.php?lang=slv&id=205178 Fakulteta za naravoslovje in matematiko 0 0 0