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We study the boundedness, the attractivity, and the stability of the positive solutions of the rational difference equation xn+1 = (pnxn-2 + xn-3)/(qn + xn-3), n = 0, 1, ..., where pn, qn, n = 0, 1, ... are positive sequences of period 2. [ABSTRACT FROM AUTHOR]

We consider the following system of Lyness-type difference equations: x1(n + 1) = (akxk(n) + bk)/ xk-1(n - 1), x2(n + 1) = (a1x1(n) + b1)/xk(n - 1), xi(n + 1) = (ai-1xi-1(n) + bi-1)/xi-2(n-1), i = 3, 4,...,k, where ai, bi, i = 1, 2,...,k, are positive constants, k ≥ 3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system. [ABSTRACT FROM AUTHOR]