The Universal Stability Law (USL): A Unified Framework for Nonlinear Pattern Formation and Stability Transitions

# Universal Stability Law (USL): Source Code and Datasets This repository contains the data and source code for the **Universal Stability Law (USL)**, a unifying framework for predicting stability transitions and pattern formation in nonlinear systems. The USL establishes that the boundary between stable and unstable regimes is governed by the dimensionless ratio **phi = F/C**, where **F** represents the driving excitation and **C** the coupling dissipation. ### Key Features:* **Theoretical Derivation:** A geometric criterion for nonlinear stability applicable across diverse domains.* **Empirical Validation:** Cross-validation against the canonical Swift-Hohenberg equation and reaction-diffusion models.* **Robustness Analysis:** Numerical evidence of the law's stability under stochastic noise, confirming a sharp transition at phi = 1.* **Multidisciplinary Applications:** Mapping of stability boundaries for morphogenesis, neural dynamics, and ecological self-organization. ### Repository Contents:1. **Python scripts:** Spectral integration of the Swift-Hohenberg equation and stochastic Langevin simulations.2. **Simulation data:** CSV files for phase maps, bifurcation analysis, and noise-scaling.3. **Diagnostic tools:** Scripts for variance analysis and front-tracking. The USL provides a cross-domain tool for predicting and controlling complex dynamics, bridging the gap between abstract bifurcation theory and empirical system behavior. ---**How to cite:**Please refer to the accompanying paper: "The Universal Stability Law (USL): A Unified Framework for Nonlinear Pattern Formation and Stability Transitions" (2026).