Dynamics of the positive solution of the max-type difference equation 〖 x〗_n=max{A,(x_(n-1)^p)/(x_(n-k)^p )}.

This study consists of five sections. In the first section, a summary of literature was given about the rational and max-type difference equations. In the second section, general definitions and theorems were given about difference equations. In the third section, studies the boundedness character, global attractivity and periodicity of the positive solutions of the difference equation x_(n+1)=A+〖x_n〗^p/〖x_(n-1)〗^p . In the forth section, studies the boundedness and global attractivity for the positive solutions of the max-type difference equation 〖 x〗_(n+1)=max{c,(x_n^p)/(x_(n-1)^p )} . In the last section, studies the dynamics of the positive solution of the max-type difference equation 〖 x〗_n=max{A,(x_(n-1)^p)/(x_(n-k)^p )} .