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Mathematics 2018, 6(1), 10; https://doi.org/10.3390/math6010010

Global Dynamics of Certain Mix Monotone Difference Equation

1
Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina
2
Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina
*
Author to whom correspondence should be addressed.
Received: 7 December 2017 / Revised: 3 January 2018 / Accepted: 7 January 2018 / Published: 12 January 2018
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications)
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Abstract

We investigate global dynamics of the following second order rational difference equation x n + 1 = x n x n 1 + α x n + β x n 1 a x n x n 1 + b x n 1 , where the parameters α , β , a , b are positive real numbers and initial conditions x 1 and x 0 are arbitrary positive real numbers. The map associated to the right-hand side of this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the corresponding parametric space. In most cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability. View Full-Text
Keywords: difference equations; equilibrium; period-two solutions; period-four solutions; global stability; monotonicity difference equations; equilibrium; period-two solutions; period-four solutions; global stability; monotonicity
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kalabušić, S.; Nurkanović, M.; Nurkanović, Z. Global Dynamics of Certain Mix Monotone Difference Equation. Mathematics 2018, 6, 10.

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