On a solvable bidimensional system of rational difference equations via Jacobsthal numbers

Ahmed Ghezal; Imane Zemmouri

doi:10.5269/bspm.68245

Ahmed Ghezal University Centre Abdelhafid Boussouf Mila: Centre Universitaire Abdelhafid Boussouf Mila
Imane Zemmouri Department of Mathematics, University of Annaba, Elhadjar 23, Annaba, Algeria.

Abstract

In this paper, we are interested in the closed-form solution of the following bidimensional system of rational of (m+1)-order, p_{n+1}=(1/(7+8q_{n-m})),q_{n+1}=(1/(7+8p_{n-m})),n,m∈N₀, and the initial values p_{-j} and q_{-j}, j∈{0,1,...,m} are real numbers do not equal -7/8. We show that the solutions of this bidimensional system are associated with Jacobsthal numbers. As a consequence, these solutions are also associated with Jacobsthal-Lucas numbers. It is shown that the global stability of positive solutions of this system holds. Our results are illustrated via numerical examples.

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