Stability of the third order rational difference equation

In this paper, we examine the global stability and boundedness of the difference equation 1 2 1 2 1 nn nn n n n xx xx x x x α β γ θ − − − − + + + = where the initial conditions 2 10 xxx , , − − are non zero real numbers and αβγ θ , , and are positive constants such that αβ γθ + ≤+ . Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.

Kaynakça

[1]. 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 −+ − + − + + = + ”. Journal of Difference Equations and Applications, 9(2), (2003), 171–199.

[15]. Camouzis E., Ladas G., Dynamics of Third - Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, (2007).

Kaynak Göster

  • ISSN: 1694-7398
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2001

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