Low-dimensional models of single neurons: A review

The paper’s quadratization section states that one Taylor-expands the current-balance and gating equations about the V-nullcline extremum (Ve, x1,e), retains up to second order in V and first order in x1, translates the extremum to the origin, and obtains dv/dt = σ a v^2 − w, dw/dt = ε[α v − λ − w] with explicit biophysical parameter mappings (their eqs. (29)–(39)). The candidate solution reproduces exactly these steps, including the definitions of v, w, and the expressions for a, α, ε, λ, gL, gj, β, ξ, and Fe, matching the paper’s formulas term-by-term. The only subtlety is that the mixed ΔV·Δx term in the V-equation is neglected; this is consistent with how the paper presents the final normal form, even though the text’s phrase “neglecting all terms with power bigger than two in V and bigger than one in x1” could be read as allowing the mixed term. Overall, the candidate faithfully mirrors the paper’s quadratization procedure and results, so both are correct and essentially the same derivation .