Global Asymptotic Behavior of

We investigate the global stability character of the equilibrium points and the period-two solutions of , 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 p...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2007; no. 1; p. 41541
Main Authors Brett, A., Kulenović, M. R. S.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 17.01.2008
Subjects
Analysis
Difference and Functional Equations
Functional Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Research Article
Ordinary Differential Equation
Functional Equation
Functional Analysis
Partial Differential Equation
Differential Equation
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Summary:We investigate the global stability character of the equilibrium points and the period-two solutions of , 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.
ISSN:1687-1847
1687-1847
DOI:10.1155/2007/41541