15
2007.
Stability of the kth Order Lyness' equation with a Period-k Coefficient
We first investigate the Lyapunov stability of the period-three solution of Todd's equation with a period-three coefficient: where α,β, and γ positive. Then for k = 2,3,… we extend our stability result to the k-order equation, where pn is a periodic coefficient of period k with positive real values and x-k+1,…,x-1, x0 ∈ (0, ∞).