What question did this study set out to answer?

To formalize a theoretical framework for viability domains in complex systems, shifting the focus from a single static equilibrium to multi-dimensional state-relation spaces capable of sustained functioning and adaptation.

August 20, 2026Open Access

Toward a Theory of Viability Domains: Formalization of Viability Domains, Constraints, and the Harmony Norm

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Authors

SHSerhii HostiuninResearch Center Borstel - Leibniz Lung Center

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Implication

Theoretical analysis formalizes viability domains and harmony norms in complex dynamical systems, suggesting a multi-state framework for system persistence and adaptive stability.

Key Points

To formalize a theoretical framework for viability domains in complex systems, shifting the focus from a single static equilibrium to multi-dimensional state-relation spaces capable of sustained functioning and adaptation.
Integrated principles from Mathematical Viability Theory, invariant safe sets, and control barrier functions to model system trajectories within bounded constraint sets.
Formulated a conceptual pipeline connecting state-relation spaces, viability constraints, mutual compatibility conditions, boundaries, and dynamic margins.
Defined viability domains as intersections of direct state admissibility conditions and mutual compatibility constraints among multi-level system components.
Formalized the Harmony Norm not as a single equilibrium point or viability kernel, but as an overarching compatibility principle across critical system variables and flows.
Established a structured operational sequence (State and Relations to Constraints, Compatibility, Viability Domain, Boundary, Margin, and Dynamics) for evaluating system robustness and regeneration.

Cite This Study

Serhii Hostiunin (2026) studied this question.

synapsesocial.com/papers/6a86b5ff8a91293e6a1cd9bd https://doi.org/10.5281/zenodo.21990016

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Implication

Theoretical analysis formalizes viability domains and harmony norms in complex dynamical systems, suggesting a multi-state framework for system persistence and adaptive stability.

Toward a Theory of Viability Domains: Formalization of Viability Domains, Constraints, and the Harmony Norm

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Implication

Key Points

Cite This Study

Toward a Theory of Viability Domains: Formalization of Viability Domains, Constraints, and the Harmony Norm

Discussion

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Implication

Key Points

Cite This Study

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