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

This work introduces the Universal Stability Law (USL), a general principle predicting stability and pattern transitions across nonlinear systems. The law defines the boundary between ordered and unstable regimes by the ratio ϕ=F/C\phi = F/Cϕ=F/C, where FFF represents driving and CCC dissipation. Using simulations of reaction–diffusion fronts, coupled-field models, and noise-driven systems, we demonstrate that F=CF=CF=C universally marks the onset of instability. The study unifies diverse domains — from morphogenesis and ecology to neural dynamics — under a single geometric criterion for nonlinear stability. All data and simulation scripts are provided for full reproducibility.