On the recursive sequence $$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}$$

AbstractThe boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}, n = 0,1,...$$ is investigated, where all the coefficients are nonnegative real numbers.