A comprehensive numerical investigation of a coupled mathematical model of neuronal excitability

The paper’s estimate (i) follows by telescoping and the triangle inequality as in (25)–(27), which is acceptable in spirit, though notation is loose. But estimate (ii) is false under the paper’s own initial condition ω0 = −0.2: at k = 1 the right-hand side is 0 while ω1 = (1−γτ)ω0 ≠ 0 by (24), and the proof incorrectly drops a positive constant when passing from “≤ 1 + τ∑ …” to “≤ τ∑ …” (cf. equations (30)–(35)). The candidate correctly identifies the failure and supplies a corrected bound including ∥ω0∥H, which is consistent with the scheme. See the statements and proofs around (22)–(27) and (30)–(35) in Section 4.2 of the paper .