Normalized Connectomes Show Increased Synchronizability with Age Through Their Second Largest Eigenvalue

The paper explicitly derives the synchronized single-node dynamics under L1 normalization (equations (27)–(29)) and the block-diagonal variational equations (39)–(41) via diagonalizing WEE, with parameters r_k = r̂_k/WE in one-to-one correspondence with the eigenvalues of the normalized LEE, and then evaluates stability by a Master Stability Function over r, exactly matching the model’s Part (a) construction and criterion . The paper further reports that near Hopf, λ_max(r) becomes positive for sufficiently large |r| and that for sufficiently large WE, λ_max(r) ≤ 0 for all |r| < 1, and links loss of synchrony to large SLE magnitude; these points align with the model’s Parts (b)–(c), which provide the same logic plus a normal-form justification near Hopf . The paper’s global SLE statements are presented empirically rather than as theorems, while the model’s writeup notes additional assumptions; nevertheless, the core derivation and stability criterion coincide.