MODELLING POLARITY-DRIVEN LAMINAR PATTERNS IN BILAYER TISSUES WITH MIXED SIGNALLING MECHANISMS

The paper proves global convergence to laminar patterns in the large-scale IO system under high polarity, a simultaneously equitable laminar partition π2, and the condition that the laminar eigenvalue λk,2 is the spectral minimum, by constructing a strongly monotone auxiliary flow and invoking irreducibility and boundedness to guarantee convergence to equilibria with contrasting layers (Theorem 3.2, supported by Lemma 3.6 and the quotient–spectrum link via π2) . It also ties instability to the IO linearization criteria (Theorem 2.1) and establishes laminar convergence on the reduced two-layer system (Theorem 3.1) . By contrast, the model’s argument incorrectly infers transverse stability of the full ODE from spectral dominance of λk,2 for the IO map, uses a center–manifold reduction not justified by the paper’s hypotheses, and asserts the existence of exactly two stable laminar equilibria without proof; none of these claims are made or needed in the paper’s monotone-systems proof .