Title

Global asymptotic behavior of yn+1 = (pyn + yn-1)/(r + qyn + yn-1)

Document Type

Article

Date of Original Version

12-1-2007

Abstract

We investigate the global stability character of the equilibrium points and the period-two solutions of yn+1 = (pyn + yn-1)/(r + qyn + yn-1), n = 0, 1,..., with positive parameters and nonnegative initial conditions. We show that every solution of the equation in the title converges to either the zero equilibrium, the positive equilibrium, or the period-two solution, for all values of parameters outside of a specific set defined in the paper. In the case when the equilibrium points and period-two solution coexist, we give a precise description of the basins of attraction of all points. Our results give an affirmative answer to Conjecture 9.5.6 and the complete answer to Open Problem 9.5.7 of Kulenović and Ladas, 2002.

Publication Title

Advances in Difference Equations

Volume

2007

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