Dynamics of the nonlinear rational difference equation $${x_{n + 1}} = {{A{x_{n - \alpha}}{x_{n - \beta}} + B{x_{n - \gamma}}} \over {C{x_{n - \alpha}}{x_{n - \beta}} + D{x_{n - \gamma}}}}$$ x n + 1 = A x n − α x n − β + B x n − γ C x n − α x n − β + D x n − γ

Abdualrazaq Sanbo (), E. M. Elsayed () and Faris Alzahrani ()
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Abdualrazaq Sanbo: King Abdulaziz University
E. M. Elsayed: King Abdulaziz University
Faris Alzahrani: King Abdulaziz University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 2, 385-401

Abstract: Abstract In this article, we study the global stability and the asymptotic properties of the non-negative solutions of the non-linear difference equation: $${x_{n + 1}} = {{A{x_{n - \alpha}}{x_{n - \beta}} + B{x_{n - \gamma}}} \over {C{x_{n - \alpha}}{x_{n - \beta}} + D{x_{n - \gamma}}}},\;\;\;\;\;n = 0,1, \ldots$$ x n + 1 = A x n − α x n − β + B x n − γ C x n − α x n − β + D x n − γ , n = 0 , 1 , … where α, β, γ are positive integers, A, B, C, D are positive real numbers and the initial conditions x−p, x−p+1, …, x−1, x0 for p = max{α, β, γ} are arbitrary positive real numbers.

Keywords: Difference equations; recursive sequences; local stability; global stability; boundedness; prime period two solution (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0333-8

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