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In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation xn+1 = α + (xn-1p / xnq), n = 0,1,..., where α, p, q ∈(0, ∞) and x-1, x0 ∈ (0, ∞). Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution. [ABSTRACT FROM AUTHOR]

We study the boundedness, the persistence and the periodicity of the non-autonomous difference equation[image omitted] with positive parameters and positive initial conditions [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]

We study the periodicity, the boundedness and the asymptotic behavior of the positive solutions of the non-autonomous difference equation: where pn, n = 0, 1,ߪ, is a positive sequence of period 3. [ABSTRACT FROM AUTHOR]

In this paper we consider the following system of partial linear homogeneous difference equations: xs(i+2,j)+asxs+1(i+1,j+1)+bsxs(i,j+2)=0,s=1,2,...,n−1,xn(i+2,j)+anx1(i+1,j+1)+bnxn(i,j+2)=0and the system of partial linear nonhomogeneous difference equations: ys(i+2,j)+asys+1(i+1,j+1)+bsys(i,j+2)=fs(i,j),s=1,2,...,n−1,yn(i+2,j)+any1(i+1,j+1)+bnyn(i,j+2)=fn(i,j)where n=2,3,..., xs(0,j)=ϕs(j), j=2,3,..., xs(1,j)=ψs(j),j=1,2,... (resp. ys(0,j)=ϕs(j), j=2,3,..., ys(1,j)=ψs(j),j=1,2,...) for the first system (resp. for the second system); as, bs, are real constants; fs:N2→R are known functions; ϕs(j),ψs(j) are given sequences; and s=1,2,...,n and the domain of the solutions of the above systems are the sets Nm={(i,j),i+j=m}, m=2,3,.... More precisely, we find conditions so that every solution of the first system converges to 0 as i→∞ uniformly with respect to j. Moreover, we study the asymptotic stability of the trivial solution of the first system. In addition, under some conditions on fs, we prove that every solution of the second system is bounded, and finally, we find conditions on fs so that every solution of the second system converges to 0 as i→∞ uniformly with respect to j. [ABSTRACT FROM AUTHOR]

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]

In this paper, we study the stability of the zero equilibria of the following 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]