Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death

The paper formulates the coupled ODE system for c, q, and W on an evolving connectome (equations (1)–(3)) and argues from simulations that "damage does not slow down disease progression" (notably Fig. 2) but does not provide a rigorous small-time asymptotic proof of first-order independence from the damage parameters β and γ . The candidate solution supplies a coherent, detailed, and correct local-in-time analysis that shows c_{β,γ}(t) − c_{0,0}(t) = O(t^3), hence o(t), with explicit bounds under the model’s assumptions. Thus, the model’s solution is correct and fills a gap left by the paper’s qualitative/numerical treatment.