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On the Dynamics of the Recursive Sequence

Yıl 2010, Cilt: 23 Sayı: 1, 53 - 59, 08.03.2010

Öz

Our aim in this paper is to investigate the local stability of the positive solutions of the difference equation

yn+1= [(α-yn)/ (βyn-1)] − [(γ-yn-1)/ βyn ] ,  n=0,1,2,...,

where the initial conditions  y−1 ,  y0 are arbitrary positive real numbers such that  yn ≠ 0 for n= −1,0,1,...,  , α, β, γ ε (0,∞)  and α > γ. Furthermore we investigate the periodic nature of the mentioned difference equation.

Key Words: Difference Equations, Local Stability, Period-two Solutions.

 

Kaynakça

  • Amleh, A.M., Grove, E.A., Ladas, G., “On the Recursive Sequencex n 1 + = α + n 1”, Journal x − xn of Mathematical Analysis and Applications, 233: 798 (1999).
  • El-Owaidy, H.M., Ahmed, A.M., Mousa, M.S., “On asymptotic behavior of the difference equationx n 1 + = α + n x and Computations, 147: 163-167 (2004).
  • DeVault, R., Kosmala, W., Ladas, G., Schultz, S.W., “Global Behavior ofy n 1 + = n n k qy+ y − Nonlinear Analysis, 47: 4743-4751 (2001).
  • He, W.S., Li, W.T., “Attractivity in a Nonlinear Delay Mathematics, E-Notes, 4: 48-53 (2004). Applied
  • Yan, X.X., Li, W.T., “Dynamic behavior of a recursive sequence”, Applied Mathematics and Computation, 157: 713-727 (2004).
  • Gibbons, C.H., Kulenović, M.R.S., Ladas, G., Voulov, H.D., “On the Trichotomy Character of xn 1= α + β ( xn+ γ xn 1) /(A+ x )”, Journal of −) /(A+ n + Difference Equations and Applications, 8 (1): 75- (2002).
Yıl 2010, Cilt: 23 Sayı: 1, 53 - 59, 08.03.2010

Öz

Kaynakça

  • Amleh, A.M., Grove, E.A., Ladas, G., “On the Recursive Sequencex n 1 + = α + n 1”, Journal x − xn of Mathematical Analysis and Applications, 233: 798 (1999).
  • El-Owaidy, H.M., Ahmed, A.M., Mousa, M.S., “On asymptotic behavior of the difference equationx n 1 + = α + n x and Computations, 147: 163-167 (2004).
  • DeVault, R., Kosmala, W., Ladas, G., Schultz, S.W., “Global Behavior ofy n 1 + = n n k qy+ y − Nonlinear Analysis, 47: 4743-4751 (2001).
  • He, W.S., Li, W.T., “Attractivity in a Nonlinear Delay Mathematics, E-Notes, 4: 48-53 (2004). Applied
  • Yan, X.X., Li, W.T., “Dynamic behavior of a recursive sequence”, Applied Mathematics and Computation, 157: 713-727 (2004).
  • Gibbons, C.H., Kulenović, M.R.S., Ladas, G., Voulov, H.D., “On the Trichotomy Character of xn 1= α + β ( xn+ γ xn 1) /(A+ x )”, Journal of −) /(A+ n + Difference Equations and Applications, 8 (1): 75- (2002).
Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Mathematics
Yazarlar

Saime Zengin Bu kişi benim

İlhan Öztürk

Fatma Bozkurt Bu kişi benim

Yayımlanma Tarihi 8 Mart 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 23 Sayı: 1

Kaynak Göster

APA Zengin, S., Öztürk, İ., & Bozkurt, F. (2010). On the Dynamics of the Recursive Sequence. Gazi University Journal of Science, 23(1), 53-59.
AMA Zengin S, Öztürk İ, Bozkurt F. On the Dynamics of the Recursive Sequence. Gazi University Journal of Science. Mart 2010;23(1):53-59.
Chicago Zengin, Saime, İlhan Öztürk, ve Fatma Bozkurt. “On the Dynamics of the Recursive Sequence”. Gazi University Journal of Science 23, sy. 1 (Mart 2010): 53-59.
EndNote Zengin S, Öztürk İ, Bozkurt F (01 Mart 2010) On the Dynamics of the Recursive Sequence. Gazi University Journal of Science 23 1 53–59.
IEEE S. Zengin, İ. Öztürk, ve F. Bozkurt, “On the Dynamics of the Recursive Sequence”, Gazi University Journal of Science, c. 23, sy. 1, ss. 53–59, 2010.
ISNAD Zengin, Saime vd. “On the Dynamics of the Recursive Sequence”. Gazi University Journal of Science 23/1 (Mart 2010), 53-59.
JAMA Zengin S, Öztürk İ, Bozkurt F. On the Dynamics of the Recursive Sequence. Gazi University Journal of Science. 2010;23:53–59.
MLA Zengin, Saime vd. “On the Dynamics of the Recursive Sequence”. Gazi University Journal of Science, c. 23, sy. 1, 2010, ss. 53-59.
Vancouver Zengin S, Öztürk İ, Bozkurt F. On the Dynamics of the Recursive Sequence. Gazi University Journal of Science. 2010;23(1):53-9.