Dynamics of some Rational Difference Equations.

The main goal of this paper is to investigate the qualitative behavior of the solutions for the following rational difference equation: ... where α, β, ai,bi ∈ (0,∞),i =0, 1, ..., k; with the initial conditions x0,x-1, ..., x-2k,x-2k-1 ∈ (0,∞). We determine the equilibrium points of the considered equation and then study their local stability. Also we study the boundedness and the permanence of the solutions. Finally we investigate the global asymptotically stable of the equilibrium points. [ABSTRACT FROM AUTHOR]