The aim of this paper is to study the global behavior of a higher order nonlinear difference equation.
The character of semicycles, periodicity, global stability and boundedness of positive solutions of the mentioned difference equation are investigated.
It is deduced that, when q<1, then the positive equilibrium of this equation is globally asymptotically stable and, when q>1, then this difference equation possesses unbounded solutions.
The paper investigates some of the characteristics of nonlinear difference equations.
Dehghan, M. and Mazrooei‐Sebdani, R. (2008), "Some characteristics of solutions of a class of rational difference equations", Kybernetes, Vol. 37 No. 6, pp. 786-796. https://doi.org/10.1108/03684920810876981
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