Generalized Lotka–Volterra Systems and Complex Balanced Polyexponential Systems

The paper proves the complex-balanced GLV results (existence/uniqueness of positive steady states per compatibility manifold and global stability) via a Lyapunov function in log-coordinates for the associated polyexponential system, then transfers them back to the GLV system. The candidate solution proves the same four statements directly in GLV/log coordinates using an alternative convexity/KL-divergence style inequality. The claims match the paper’s Theorem 4.6 and the logic aligns with the paper’s Lemma 3.7 and invariance Lemma 4.1. No missing hypotheses were used beyond complex balance at x*, and the steps are consistent.