### QUALITATIVE BEHAVIOR FOR A CLASS OF NONLINEAR DIFFERENCE EQUATION

#### Abstract

We study the Stability, the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear di§erence equation xn+1 = a + Pk i=0 cixni=bxn` + dxnk: where the the initial conditions xr; xr+1; :::; x0 are arbitrary positive real numbers such that r = max f`; kg where i; r 2 f0; 1; :::g and a; b; d; ci are positive constants.

#### Keywords

di§erence equation, Stability, Periodicity, boundedness, global Stability

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