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In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations. [ABSTRACT FROM AUTHOR]

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]