Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

Murad Khan Hassani (), Yasin Yazlik, Nouressadat Touafek, Mohammed Salah Abdelouahab, Mouataz Billah Mesmouli and Fatma E. Mansour
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Murad Khan Hassani: Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir 50300, Turkey
Yasin Yazlik: Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir 50300, Turkey
Nouressadat Touafek: LMAM Laboratory, Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel 18000, Algeria
Mohammed Salah Abdelouahab: Laboratory of Mathematics and Their Interactions, Abdelhafid Boussouf University Center of Mila, Mila 43000, Algeria
Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Fatma E. Mansour: Department of Physics, College of Science and Arts in Methneb, Qassim University, Methneb 51931, Saudi Arabia

Mathematics, 2023, vol. 12, issue 1, 1-17

Abstract: In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence of the solutions and the global asymptotic stability of the unique equilibrium point of the proposed system under certain parametric conditions. Finally, for this system, we offer some numerical examples which support our analytical results.

Keywords: system of rational difference equations of order k + 1; semi-cycle analysis; boundedness and persistence; global asymptotic stability; rate of convergence; sequence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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