Ubiquity of Uncertainty in Neuron Systems

The paper demonstrates, via five coupled neuron-map models, the coexistence of chaotic and nonchaotic attractors and estimates 0 < u < 1 from final-state uncertainty, explicitly invoking d = n − u and showing nearly riddled basins for slow–fast systems; it also derives an Sb scaling that implies the ln(Sb)–ln(ε) slope agrees with u under an equiprobability assumption (Sb = s ln(NA) ε^u) . However, the paper does not prove that u can be made arbitrarily small (it gives a heuristic slow–fast explanation and numerical examples, not a general theorem) . The model’s Phase‑2 solution correctly formalizes items (i) and (iii) and cites standard results, but its claim that, under slow–fast structure, u can be tuned below any ε*>0 (via intermittency/blowout) requires additional, unproved hypotheses for these neuron maps. Hence both are incomplete with respect to the tunability claim, while they align on existence (0 < u < 1) and the basin‑entropy slope = u statement.