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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References

R. Abo-Zeid., C. Cinar. Global behavior of the difference equation x_{n+1}=┊Ax_{n-1}/B-Cx_{n}x_{n-2}. Boletim da Sociedade Paranaense de Matemática, 31(1), 43-49 (2013).

E. M. Elsayed., H. S. Gafel. On the solutions and behavior of rational systems of difference equations. Boletim da Sociedade Paranaense de Matemática, Articles in Press.

A. Ghezal., I. Zemmouri. Higher-order system of p-nonlinear difference equations solvable in closed-form with variable coefficients. Boletim da Sociedade Paranaense de Matemática, 41, 1-14 (2022).

A. Ghezal. Note on a rational system of (4k+4)-order difference equations: periodic solution and convergence. Journal of Applied Mathematics and Computing, (2022), https://doi.org/10.1007/s12190-022-01830-y.

A. Ghezal., I. Zemmouri. Solution forms for generalized hyperbolic cotangent type systems of p-difference equations. Boletim da Sociedade Paranaense de Matemática, Accepted.

A. Ghezal., I. Zemmouri. On solutions of a two-dimensional (m+1)-order system of difference equations via Pell numbers. Boletim da Sociedade Paranaense de Matemática, Submit.

A. Ghezal., I. Zemmouri. Global stability of a multi-dimensional system of rational difference equations of higher-order with Pell-coefficients. Boletim da Sociedade Paranaense de Matemática, Submit.

A. Ghezal., I. Zemmouri. Convergence of solutions of a p-dimensional system of sk-order rational recursive equations. Boletim da Sociedade Paranaense de Matemática, Submit.