Abstract
<jats:p>Generalized Lotk–Volterra (GLV) systems, with roots in ecology, constitute one of the most studied classes of positive ODEs. Recently, a reaction-network perspective for a generalization useful in mathematical epidemiology, called block GLV systems, was offered by Adenane, Avram and Halanay (2026). These authors offer a "siphon calculus" in which the boundary stability of block GLV equations is determined by studying (i) invariant faces associated to minimal siphons, (ii) transversal Jacobians, (iii) invasibility expressed via R-invasion functions, (iv) relay graphs (v) exclusion partitions and (vi) Lyapunov functions, without leaving the original state space. Another reaction-network perspective for GLV systems was offered by Rojas La Luz, Yu and Craciun, who developed a global stability theory for positive equilibria by introducing associated poly-exponential systems obtained through the logarithmic change of variables $x_i=e^{\xi_i}$. In these logarithmic coordinates, compatibility classes become affine subspaces and remarkably simple quadratic Lyapunov functions establish global convergence of complex-balanced systems. The purpose of the present paper is to combine the two perspectives. We revisit examples considered by Rojas La Luz, Yu and Craciun, where the use of siphon calculus can be avoided, but we still find it useful, at least for suggesting open problems for block GLV systems.</jats:p>