In the latest Beyond the Edge seminar, Tiago P. Peixoto presented recent work entitled “Graphs are maximally expressive for higher-order interactions” (with Leto Peel, Thilo Gross, and Manlio De Domenico).
Watch it here: https://youtu.be/2Czu8Bf9qWw?si=9r0Xfnj3ieIQzVIH
This study examines whether structural-dynamical indicators provide earlier detection of fisheries collapse than classical reference-point metrics such as fishing pressure (F/F_MSY) and spawning stock biomass (SSB/B_MSY). While these traditional indicators achieve near-perfect classification performance in datasets with strong separation between collapsed and stable stocks, they encode system state rather than trajectory. Using 46 stock trajectories calibrated to the RAM Legacy Stock Assessment Database and focusing explicitly on the early-phase regime (10–20 years prior to collapse), we evaluate two dynamical indicators: the lag-1 autocorrelation of fishing pressure (X3) and the log-rate of change of relative spawning biomass (X5). Discrimination performance (AUC) is saturated across all models and therefore uninformative. Instead, we assess predictive value through lead-time analysis. We find that X3 and X5 detect impending collapse a mean of 7.6 and 9.0 years earlier, respectively, than classical reference-point indicators (p < 0.001). Operational deployment requires persistence filtering of at least four consecutive years to control false positives, under which X5 achieves a false-positive rate of 0.091 while retaining substantial lead-time advantage. These results indicate that dynamical indicators provide a complementary early-warning layer whose contribution is temporal rather than discriminative, shifting the evaluation of collapse prediction from classification performance to temporal detectability. The framework is not a replacement for classical fisheries metrics but an extension that captures trajectory-level information preceding threshold crossing. Keywords: early-warning signals, fisheries collapse, critical slowing down, lead-time detection, stock assessment, dynamical systems, regime shifts, ecological forecasting
This month, CTCS (IIT Madras) & @PIK_climate present a webinar:
📢: The asymptotic state of decaying turbulence
🎙️: Prof. K. R. Sreenivasan, New York University
📅: March 30 |⏰ 19:30 IST | 16:00 CEST | 10:00 EDT
🔗: https://us06web.zoom.us/webinar/register/WN_0BicRp5MTFqu8Yf3I2jCcQ
#Complexsystems #phd #computationalfluiddynamics #Turbulence #NonlinearDynamics #Bifurcations #NYU #ITCP #PIK #webinarinvite #Zoomcodes #ComplexNetworks #MachineLearning #fluidmechanics
This paper presents Version 4 of the Singularization Framework, a minimal dynamical theory of structural collapse in complex adaptive systems. The framework introduces three state variables — Structural Compression C(t), Adaptive Resonance R(t), and Systemic Tension T(t) — forming the Compression–Resonance–Tension Index (CRTI).The central contribution is the analytic derivation of the collapse region from system dynamics. The C–R subsystem is shown to undergo a saddle-node bifurcation at the critical parameter κ = αγ/(δ_C β) = 1, at which the healthy equilibrium annihilates with the separatrix saddle, leaving the collapse attractor P₃ = (1, 0) as the sole stable fixed point. The collapse basin Ω_c is defined as the basin of attraction of P₃, bounded by the stable manifold of the saddle — replacing the ad-hoc threshold definitions of previous versions.A stochastic Langevin extension connects the framework to Kramers escape rate theory, providing quantitative collapse probability estimates. Near the bifurcation, classical critical slowing down signatures are analytically guaranteed: rising variance, rising lag-1 autocorrelation, and diverging recovery time. A fragility index φ = |κ − 1| provides an operationalisable systemic vulnerability criterion.The framework is positioned relative to May’s fold catastrophe model, Scheffer–Dakos early warning signal theory, Freidlin–Wentzell quasi-potential theory, and Ashby’s Law of Requisite Variety. Empirical proxies for C, R, and T are proposed across organisational, ecological, financial, and physiological domains. complex adaptive systems · structural collapse · bifurcation theory · saddle-node bifurcation · critical transitions · early warning signals · critical slowing down · stochastic dynamics · Kramers escape rate · resilience theory · CRTI · Singularization Framework · nonlinear dynamics · quasi-potential · Lyapunov function · adaptive resonance · structural compression · systemic tension · complexity science · panarchy
This paper introduces and positions the Singularization Framework, a conceptual model for collapse dynamics in complex adaptive systems. The framework proposes that systemic collapse is driven primarily by endogenous structural compression and the progressive loss of adaptive resonance, rather than by external shocks alone. Central contributions include: (1) The Mallinckrodt Cycle — a five-phase lifecycle model (Expansion, Integration, Compression, Brittleness, Collapse/Singularization) extending Holling's adaptive cycle by disaggregating the conservation phase into diagnostically distinct sub-phases. (2) Adaptive Resonance as a stabilizing mechanism — the system's capacity to maintain oscillatory adaptability across its configuration space. (3) Resonance Collapse as a novel collapse category distinct from bifurcation-based tipping points. (4) The Compression–Resonance–Tension Index (CRTI) — a proposed three-dimensional early-warning diagnostic operating at Phase III, prior to the bifurcation point detected by existing indicators. The framework is positioned against Holling's Panarchy, Scheffer's critical transitions theory, Truong et al.'s entropy collapse model (arXiv:2512.12381), Taleb's antifragility, and Kauffman's NK models. Three structural gaps in existing literature are identified and addressed. Classification: Known components, new synthesis — with substantive novelty in the Resonance Collapse mechanism and CRTI diagnostic concept. complex systemsstructural compressionadaptive capacityresonance collapsesingularizationCRTIMallinckrodt Cyclecollapse dynamicscomplex adaptive systemsearly warning signalspanarchycritical transitionsentropy collapseresilience theoryconfiguration space
This paper introduces the Mallinckrodt Cycle, a theoretical framework describing a recurrent collapse mechanism in complex adaptive systems. The central argument is that systemic failure arises not primarily from external shocks or disorder, but from internal processes of structural compression that progressively reduce a system’s effective configuration space and oscillatory flexibility.The framework formalizes five phases: Expansion, Integration, Compression, Brittleness, and Collapse (Singularization). A conceptual energy equation (E = S · S_max²) is proposed to formalize the relationship between realized entropy, potential configuration space, and systemic adaptive potential. The Compression–Resonance–Tension Index (CRTI) is introduced as a composite diagnostic indicator for early warning detection of Phase III–IV dynamics.The framework is positioned relative to resilience theory (Holling, Panarchy), critical transition theory (Scheffer, Dakos), antifragility (Taleb), and recent entropy-collapse literature (Truong et al., 2025). It does not claim the status of a universal physical law but offers a formal conceptual scaffold for cross-domain analysis of structural fragility in ecological, organizational, economic, and social systems. complex adaptive systems structural compression adaptive capacity resonance collapse Mallinckrodt Cycle CRTI Compression-Resonance-Tension Index singularization systemic fragility critical transitions resilience theory panarchy antifragility entropy collapse early warning signals phase transitions complexity science systems theory nonlinear dynamics organizational resilience
This preprint presents a simulation-based proof of concept for the Compression–Resonance–Tension Index (CRTI), a minimal dynamical framework proposed to diagnose structural fragility in complex adaptive systems. The CRTI model links three state variables — structural compression (C), adaptive resonance (Res), and systemic tension (T = C/Res) — through a coupled nonlinear ODE system. Numerical simulations demonstrate three qualitatively distinct dynamical regimes: stable equilibria, near-threshold dynamics, and resonance collapse. A bifurcation analysis identifies a sharp nonlinear transition at γ/ρ = 1, arising endogenously from the fixed-point structure of the resonance equation rather than from an externally imposed parameter. The reduced resonance equation belongs structurally to the class of fold bifurcation models used in resilience theory, and the slow–fast decomposition of the full system corresponds to established tipping-point formulations. A sensitivity analysis confirms that the bifurcation threshold is robust to ±20% parameter variation, with the critical ratio γ/ρ remaining within ±15% of unity across all tested perturbations. The model is intentionally minimal and empirically uncalibrated. Its purpose is to demonstrate that the proposed compression–resonance interaction generates mathematically tractable, collapse-like dynamics consistent with regime-shift behavior observed in ecological, organizational, and socio-technical systems. All simulation code is provided as supplementary material to ensure full computational reproducibility. This preprint has not undergone peer review. complex adaptive systemsnonlinear dynamicsbifurcation analysisresilience theorystructural fragilityregime shiftstipping pointsearly warning signalssystemic riskcollapse dynamicscompression-resonance-tension indexCRTIfold bifurcationLotka-Volterracomplexity science
This preprint presents a simulation-based proof of concept for the Compression–Resonance–Tension Index (CRTI), a minimal dynamical framework proposed to diagnose structural fragility in complex adaptive systems. The CRTI model links three state variables — structural compression (C), adaptive resonance (Res), and systemic tension (T = C/Res) — through a coupled nonlinear ODE system. Numerical simulations demonstrate three qualitatively distinct dynamical regimes: stable equilibria, near-threshold dynamics, and resonance collapse. A bifurcation analysis identifies a sharp nonlinear transition at γ/ρ = 1, arising endogenously from the fixed-point structure of the resonance equation rather than from an externally imposed parameter. The reduced resonance equation belongs structurally to the class of fold bifurcation models used in resilience theory, and the slow–fast decomposition of the full system corresponds to established tipping-point formulations. A sensitivity analysis confirms that the bifurcation threshold is robust to ±20% parameter variation, with the critical ratio γ/ρ remaining within ±15% of unity across all tested perturbations. The model is intentionally minimal and empirically uncalibrated. Its purpose is to demonstrate that the proposed compression–resonance interaction generates mathematically tractable, collapse-like dynamics consistent with regime-shift behavior observed in ecological, organizational, and socio-technical systems. All simulation code is provided as supplementary material to ensure full computational reproducibility. This preprint has not undergone peer review. complex adaptive systemsnonlinear dynamicsbifurcation analysisresilience theorystructural fragilityregime shiftstipping pointsearly warning signalssystemic riskcollapse dynamicscompression-resonance-tension indexCRTIfold bifurcationLotka-Volterracomplexity science
Manlio De Domenico
BeyondTheEdge - MSCA Network
Bernd von Mallinckrodt 🦋
Prof. R. I. Sujith