Constraint-Coupled Reaction–Diffusion Systems: Viability, Endogenous Regulation, and Dynamically Generated Localization
Year: 2026
Type: article
Abstract: We introduce a deterministic class of constraint-coupled reaction–diffusion systems in which an internally generated field modulates transport and reaction processes while being regenerated by the same dynamics that it regulates. This feedback structure provides a minimal mathematical framework for studying organizational self-maintenance in spatially extended non-equilibrium systems. The model is formulated as a quasilinear parabolic system on a bounded domain. Positivity, boundedness, viability, equilibrium stability, and spatial localization are treated as distinct mathematical properties. Under structural assumptions on the diffusion and reaction terms, we establish local classical well-posedness, preservation of non-negativity, and global existence under boundedness or forward-invariant-region conditions. Viability is formulated as forward invariance of subsets of an infinite-dimensional phase space rather than as a local pointwise balance. A minimal three-field realization, consisting of a resource field, an organizing field, and a constraint field, is then analyzed. We derive conditions for the existence of positive homogeneous equilibria, obtain sufficient criteria for homogeneous and full modal stability, and characterize stationary and oscillatory spatial instability thresholds through a mode-dependent dispersion relation. We complement the analysis with conservative two-dimensional finite-volume simulations. Below the predicted spatial-instability threshold, perturbations decay, whereas above threshold a persistent heterogeneous state forms with a dominant scale consistent with the dispersion relation. Constraint level sets, occupied fraction, connected components, and concentration indices quantify the resulting dynamically generated localization. The framework distinguishes externally imposed regulation from internally generated constraints and provides a rigorous basis for investigating bounded self-maintenance, spatial instability, and dynamically generated localization in nonlinear reaction–diffusion systems.
Source: Dynamics
Authors: Cécile Barbachoux, Joseph Kouneiher
Institution: Université Côte d'Azur
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W7204487464