On the Trichotomy Character of x n +1 =(α+β x n +γ x n −1 )/( A + x n )

By C. H. Gibbons, Mustafa R. S. Kulenovic, G. Ladas, H. Voulov. 2002

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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 .

Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health

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