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1. 1. 2002.
On the Trichotomy Character of x n +1 =(α+β x n +γ x n −1 )/( A + x n )
We show that the equation in the title with nonnegative parameters and nonnegative initial conditions exhibits a trichotomy character concerning periodicity, convergence, and boundedness which depends on whether the parameter n is equal, less, or greater than the sum of the parameters g and A .