Search

In this paper we study the non-autonomous logistic difference equation[image omitted] with the nonnegative initial conditions x- 1, x0. In particular, the periodic behavior, the attractivity of solutions and the stability of solutions are discussed in detail. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the qualitative behavior of solutions of the class of delay difference equationwhere the initial conditions x −2k+1,…, x −1, x 0 are positive, k ∈{1,2,…}, and the parameters β, γ, A, B are positive. Our concentration is on invariant intervals and the global stability of the above mentioned equation. We obtain sufficient conditions for the global attractivity of all positive solutions about the zero and positive equilibrium points with basins that depend on specific conditions posed on the coefficients. Furthermore, the oscillation and the character of semicycles about the positive equilibrium are thoroughly discussed. It is also illustrated that for some special case of parameters, the solution will be either a period-2 solution, or will converge to the equilibrium point, or will have unbounded solutions. [Copyright &y& Elsevier]

Abstract: Our aim in this paper is to investigate the global asymptotic stability of all positive solutions of the higher order nonlinear difference equation xn+1=α+βxn-k+1+γxn-2k+1Bxn-k+1+Cxn-2k+1, n=0,1,2,… where B, C and α, β, γ are positive, k ∈{1,2,3,…}, and the initial conditions x −2k+1,…, x −1, x 0 are positive real numbers. We show that the unique positive equilibrium of the equation is globally asymptotically stable and has some basins that depend on certain conditions posed on the coefficients. Our concentration is on invariant intervals, the character of semicycles, and the boundedness of the above mentioned equation. Our final comments are about informative examples. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the qualitative behavior of solutions to the difference equationwhere the initial conditions x −k ,…, x −1, x 0 are non-negative, k ∈{1,2,3,…}, and the parameters p, q are non-negative. Our concentration is on invariant intervals, the character of semicycles, the global stability, and the boundedness of the above mentioned equation. It is worth to mention that this difference equation was an open problem introduced by Kulenovic and Ladas in [M.R.S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, Boca Raton, 2002.]. Our final comments are about informative examples. [Copyright &y& Elsevier]