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Global attractivity of a higher-order nonlinear difference equation. (English) Zbl 1201.39006

Authors’ abstract: The main goal of this paper is to investigate the locally asymptotically stable, period-two solutions, invariant intervals and global attractivity of all negative solutions of the nonlinear difference equation

x n+1 =1-x n A+x n-k ,n=0,1,,

where A(-,-1),k is a positive integer and initial conditions x -k ,,x 0 (-,0]. It is shown that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient

MSC:
39A20Generalized difference equations
39A30Stability theory (difference equations)
39A22Growth, boundedness, comparison of solutions (difference equations)
References:
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