What question did this study set out to answer?

The research aims to develop a unified framework to understand delayed homeostasis in oscillating and collapsing systems across multiple disciplines.

April 4, 2026Open Access

"Delayed Homeostasis: A Unified Framework for Oscillations and Collapse in Regulated Systems with Memory"

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Key Points

The research aims to develop a unified framework to understand delayed homeostasis in oscillating and collapsing systems across multiple disciplines.
Defined the mathematical model dX/dt=P−L(X(t−τ)) with parameters for oscillation and collapse.
Analyzed soft memory models for stability across different systems.
Examined the application of the framework in areas like patient monitoring and AI hallucination detection.
Identified a universal homeostatic index H that indicates system stability and health.
Demonstrated that the delayed-loss formulation effectively captures behavior in multiple disciplines and timescales.
Established connections between multi-loop coupling and system failures in various regulated systems.

Abstract

Delayednegativefeedbackisubiquitousinregulatedsystems frombloodcellproductiontotokamakplasmas, fromneuralmotorcontrol tointernetcongestion.Weshowthat all suchsystems shareasinglemathematical backbone: dX/dt=P−L(X(t−τ)),with aHopf bifurcationat τh=π/(2A) andauniversal homeostatic indexH=τh/τeff. We provethatthewidely-used softmemory modelk(X(t−τ)−X(t))isunconditionallystable (Hayes1950), explainwhythiserrorpersistsacrossdisciplines, anddemonstratethat the delayed-lossformulationcapturesoscillations,relaxationcycles,andcascadecollapseinseven domainsspanning10ordersofmagnitude intimescale. The indexHprovidesareal-time healthmetric:H>2(robust),H≈1(oscillations),H<1(collapse).Multi-loopcoupling explainswhycascade failures (disruptions, organfailure, nancial crises)propagateacross timescales.Applicationstoreal-timepatientmonitoringinintensivecareandtohallucinationdetectioninlarge languagemodelsareoutlined. Nonewmathematics isclaimed; the contributionistheinterdisciplinarysynthesisitself.

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Olivier Lane-Larquey (Thu,) studied this question.

synapsesocial.com/papers/69d0ae94659487ece0fa48cb — DOI: https://doi.org/10.5281/zenodo.19387108

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"Delayed Homeostasis: A Unified Framework for Oscillations and Collapse in Regulated Systems with Memory"

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