In this paper, we examine the global stability and boundedness of the differenceequation1 21 21nn nnn nnxx xxx x xα βγ θ− −− −+++ =where the initial conditions 2 10 xxx , , − − are non zero real numbers and αβγ θ , , andare positive constants such thatαβ γθ + ≤+ .Also, we discuss and illustrate the stability of the solutions of the considered equationvia MATLAB at the end of study to support our results.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, we examine the global stability and boundedness of the differenceequation1 21 21nn nnn nnxx xxx x xα βγ θ− −− −+++ =where the initial conditions 2 10 xxx , , − − are non zero real numbers and αβγ θ , , andare positive constants such thatαβ γθ + ≤+ .Also, we discuss and illustrate the stability of the solutions of the considered equationvia MATLAB at the end of study to support our results.
📊
Key Findings & Data:In this paper, we examine the global stability and boundedness of the differenceequation1 21 21nn nnn nnxx xxx x xα βγ θ− −− −+++ =where the initial conditions 2 10 xxx , , − − are non zero real numbers and αβγ θ , , andare positive constants such thatαβ γθ + ≤+ .Also, we discuss and illustrate the stability of the solutions of the considered equationvia MATLAB at the end of study to support our results.
💡
Conclusion & Impact:In this paper, we examine the global stability and boundedness of the differenceequation1 21 21nn nnn nnxx xxx x xα βγ θ− −− −+++ =where the initial conditions 2 10 xxx , , − − are non zero real numbers and αβγ θ , , andare positive constants such thatαβ γθ + ≤+ .Also, we discuss and illustrate the stability of the solutions of the considered equationvia MATLAB at the end of study to support our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we examine the global stability and boundedness of the differenceequation1 21 21nn nnn nnxx xxx x xα βγ θ− −− −+++ =where the initial conditions 2 10 xxx , , − − are non zero real numbers and αβγ θ , , andare positive constants such thatαβ γθ + ≤+ .Also, we discuss and illustrate the stability of the solutions of the considered equationvia MATLAB at the end of study to support our results.
🔖
Cite This Article
Erdogan, M. E. (2022). Stability of the third order rational difference equation. Manas Journal of Engineering, Cilt: 8 - Sayı: 1, 68–76. https://ajindex.com/articles/578020
. Yang X., “On the global asymptotic stability of the difference equation 12 3 1 23 nn n n n nn xx x a x x xx a −− − − −− + + = + + ”, Applied Mathematics and Computation, 171(2), (2005), 857–861. [2]. Kulenović M.R.S., Ladas G., Sizer W.S., “On the recursive sequence 1 1 1 n n n n n x x x x x α β γ δ − + − + = + ”, Mathematical Sciences Research Hot-Line, 2(5), (1998), 1–16. [3]. Elabbasy E.M., El-Metwally H.A., Elsayed E.M., “Global behavior of the solutions of some difference equations”, Advances in Difference Equations, 1, (2011), 28. [4]. Khaliq A., Elsayed E.M., “Qualitative study of a higher order rational difference equation”, Hacettepe Journal of Mathematics and Statistics, 47(5), (2018), 1128–1143. [5]. Erdogan M.E., Cinar C., Yalcinkaya I., “On the dynamics of the recursive sequence 1 1 2 2 24 24 n n nn nn x x βγ γ xx xx − + −− −− = + + ”, Computers & Mathematics with Applications, 61(3), (2011), 533-537. [6]. Erdogan M.E., Cinar C., Yalcinkaya I., “On the dynamics of the recursive sequence 1 1 2 2 1 1 n n t t nk nk k k x x x x α β γ − + − − = = = + ∑ ∏ ”, Mathematical and Computer Modelling, 54(5), (2011), 1481-1485. [7]. Erdogan M.E., Cinar C., “On the dynamics of the recursive sequence 1 1 2 2 1 1 n n t t p q nk nk k k x x x x α β γ − + − − = = = + ∑ ∏ ”, Fasciculi Mathematici, 50, (2013), 59-66. [8]. Abo-Zeid R., Al-Shabi M.A., “Global Behavior of a third order difference equation”, Tamkang Journal of Mathematics, 43(3), (2012), 375-383. [9]. Agarwal R.P., Difference Equations and Inequalities: Theory, Methods, and Applications, Chapman & Hall/CRC Pure and Applied Mathematics, (2000). [10]. Karakostas G.L., “Convergence of a Difference Equation Via The Full Limiting Sequences Method”, Differential Equations and Dynamical Systems, 1(4), (1993), 289–294. [11]. Belhannache F., Touafek N., Abo-Zeid R., “Dynamics of a third-order rational difference equation”. Bulletin Mathematique de La Societe Des Sciences Mathematiques de Roumanie, 59(1), (2016), 13–22. [12]. Hamza A.E., Ahmed A.M., Youssef A.M., “On the recursive sequence 1 1 n n k n a bx x A Bx + − + = + ”, Arab Journal of Mathematical Sciences, 17(1), (2011), 31–44. [13]. Hamza A.E., Elsayed E.M., “Stability problem of some nonlinear difference eqauations”, International Journal of Mathematics and Mathematical Sciences, 21(2), (1998), 331–340. [14]. Grove A.E., Ladas G., Predescu M., Radin M., “On the Gloval Character of the Difference Equation (2 1) 2 1 2 n k nl n n l x x x A x αγ δ −+