Self-Organized Criticality from Protected Mean-Field Dynamics: Loop Stability and Internal Renormalization in Reflective Neural Systems

TL;DR

This paper demonstrates that reflective homeostatic neural dynamics inherently produce self-organized criticality through a protected mean-field critical surface, stabilized by internal mechanisms and adaptive responses without external tuning.

Contribution

It introduces a field-theoretic framework showing how fluctuation effects are regularized, leading to robust criticality in neural systems through internal adaptation and loop renormalization.

Findings

Loop corrections are dynamically regularized by homeostatic curvature.

The critical surface remains marginally stable under coarse-graining.

Intrinsic parameter flows attract the system to criticality without external tuning.

Abstract

The reflective homeostatic dynamics provides a minimal mechanism for self-organized criticality in neural systems. Starting from a reduced stochastic description, we demonstrate within the MSRJD field-theoretic framework that fluctuation effects do not destabilize the critical manifold. Instead, loop corrections are dynamically regularized by homeostatic curvature, yielding a protected mean-field critical surface that remains marginally stable under coarse-graining. Beyond robustness, we show that response-driven structural adaptation generates intrinsic parameter flows that attract the system toward this surface without external fine tuning. Together, these results unify loop renormalization and adaptive response in a single framework and establish a concrete route to autonomous criticality in reentrant neural dynamics.