GLOBAL DYNAMICAL BEHAVIOURS AND PERIODICITY OF A CERTAIN QUADRATIC-RATIONAL DIFFERENCE EQUATION WITH DELAY
Erkan Tasdemir, Melih Gocen, Yueksel Soykan
article (Uluslararası, Hakemli) | Yazar(lar): Erkan Tasdemir, Melih Gocen, Yueksel Soykan | Yıl: 2022 | Dergi/Kurum: MISKOLC MATHEMATICAL NOTES | İndeks: WOS.SCI | DOI: 10.18514/mmn.2022.3996 | Anahtar Kelimeler: Difference equations, periodicity, boundedness, semi-cycle, global asymptotic stability, rate of convergenc
Our aim in this paper is to deal with the dynamics of following higher order difference equation
x(n+ 1) = A+ B x(n- m)/x(n)(2)
where A, B > 0, and initial values are positive, and m = {1,2,...}. Furthermore, we discuss the periodicity, boundedness, semi-cycles, global asymptotic stability of solutions of these equations. We also handle the rate of convergence of solutions of these difference equations.