Adaptive Coherence Control in Stratified Non-Gradient Dynamical Systems: A Barrier Lyapunov Framework with Pseudo-Arclength Bifurcation Continuation

Created using AI : This dataset contains a computational framework for the analysis and control of nonlinear dynamical systems derived from Galerkin-reduced reaction–diffusion equations. The framework includes: - a finite-dimensional reduction of a reaction–diffusion PDE using Fourier/Galerkin projection - a barrier Lyapunov feedback control method ensuring forward invariance of the state space - a Newton–Krylov pseudo-arclength continuation algorithm for tracking equilibria through saddle-node bifurcations The code produces reproducible numerical experiments including stability verification and continuation through bifurcation points. All results are deterministic (fixed seed = 42) and fully reproducible. This release includes code, numerical routines, figures, and manuscript source files.