Nonlinear TLMM Framework v4.1: Parameter Identification, Colored Noise Dynamics, and Robust Adaptive Neuromodulation

This repository accompanies the preprint: Nonlinear TLMM Framework v4.1: Parameter Identification, Colored Noise Dynamics, and Robust Adaptive Neuromodulation Version 4.1 extends the nonlinear Threshold-Limited Mode Modulation (TLMM) framework from an adaptive stochastic operating-region control theory into an identifiable, robustness-aware, and partially personalized framework for structural suppression dynamics. The framework integrates: adaptive TLMM dynamics stochastic closure through Fokker–Planck dynamics adaptive synchronization control network-level propagation robustness analysis under structural-connectivity uncertainty colored-noise dynamics using Ornstein–Uhlenbeck processes parameter identification and digital-twin construction simulation-based clinical translation quantitative falsifiability criteria A major conceptual advance of v4.1 is the transition from: “Where does structural suppression exist?” to: “How can structural suppression be estimated, maintained, personalized, and robustly controlled under realistic noise and uncertainty?” The framework introduces: bounded optimum robustness landscapes stochastic uncertainty bands τ_c-dependent colored-noise falsifiability criteria observation-operator specification H(E)=E² parameter-identification architecture for adaptive digital twins robustness-aware adaptive protocol construction Figures 1–9 summarize the framework, including adaptive control architecture, stochastic closure, synchronization tracking, network-level propagation, simulation and clinical translation, unified theoretical structure, stochastic robustness analysis, colored-noise dynamics, and parameter-identification pipelines. Important note: All numerical values, simulations, uncertainty bands, clinical scores, case-study panels, and performance metrics are illustrative model outputs generated from simplified mathematical assumptions. They are not derived from clinical datasets and should not be interpreted as clinical evidence, therapeutic validation, or medical decision support. This framework remains exploratory and theoretical. Future work includes: experimental electrophysiological validation structural identifiability analysis parameter fitting to real datasets nonlinear control optimization MPC / Lyapunov-based adaptive control patient-specific adaptive neuromodulation