We study coupled discrete-time systems of Kronecker-sum type M = Iₘ ⊗ A + C ⊗ Iₙ where A is the internal dynamics and C is the coupling operator. We introduce the dimensionless Coupling Collapse Index Icc (A, C) = ||C||₂ R∞ (A) and prove that the condition Icc (A, C) < 1 yields a resolvent bound, a Kreiss constant bound, and a transient amplification bound. The result is sharp for normal A, conservative for non-normal A, and extends naturally to heterogeneous agent populations.
Vladimir Telehanič (Sun,) studied this question.