Some Characteristics of the Closed-Form Solutions of Two Nonlinear Difference Equations

摘要

We derive the closed-form solutions of the following difference equations x_(n+1) = x_(n-3)/(±1 + x_(n-2)x_n), n = 0,1,2,..., where x_(-3), x_(-2), x_(-1), x_0 ∈ (0,∞). We also investigate the behavior of their respective solutions. Particularly, we study the convergence, periodicity character, stability and boundedness of their solutions.