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Recently, mathematicians have been interested in studying the theory ofdiscrete dynamical system, specifically difference equation, such thatconsiderable works about discussing the behavior properties of its solutions(boundedness and unboundedness) are discussed and published in many areas ofmathematics which involves several interesting results and applications inapplied mathematics and physics ,One of the most important discrete dynamicswhich is become of interest for researchers in the field is the rationaldynamical system .In this paper we may discuss qualitative behavior andproperties of the difference equation $x_{n+1}=ax^2_{n}+bx^2_{n-1}$ with $a$and $b$ are two parameters and we shall show its application to medicine.

On the Boundedness solutions of the difference equation $x_{n+1}=a x^\alpha_{n}+bx^\alpha_{n-1},0<\alpha \leq2$ and its application in medicine