Global Dynamics of Certain Mix Monotone Difference Equation

Senada Kalabušić, Mehmed Nurkanović and Zehra Nurkanović
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Senada Kalabušić: Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina
Mehmed Nurkanović: Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina
Zehra Nurkanović: Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina

Mathematics, 2018, vol. 6, issue 1, 1-13

Abstract: We investigate global dynamics of the following second order rational difference equation x n + 1 = x n x n ? 1 + ? x n + ? x n ? 1 a x n x n ? 1 + b x n ? 1 , where the parameters ? , ? , 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.

Keywords: difference equations; equilibrium; period-two solutions; period-four solutions; global stability; monotonicity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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