Input Driven Synchronization of Chaotic Neural Networks with Analyticaly Determined Conditional Lyapunov Exponents

Core claims in the paper—existence of a synchronous solution under zero row-sums, the master-stability reduction, and the conditional spectrum li = −1 + Re(λi) q—match the model’s solution outline and derivation. The paper’s MSF-based linearization and block-diagonalization arguments, and the l0 bookkeeping, are consistent with the model’s treatment . However, the paper incorrectly asserts that boundedness 0 ≤ ϕ′(x) ≤ M implies the existence of the time-average q via the squeeze theorem, which is false in general (boundedness alone does not ensure a Cesàro limit). The model explicitly conditions its formulae on the existence of q (e.g., periodic xs), thereby patching this gap. The paper also states a non-strict stability inequality µi ≤ 1/q (where strict negativity of exponents is needed for local asymptotic stability), whereas the model uses the standard strict criterion max Re(λi) < 1/q. Aside from these issues, both follow substantially the same proof strategy; the model is careful about missing hypotheses and boundary cases, so we judge the paper as incomplete and the model as correct.