BibTex RIS Kaynak Göster

xn+1 = xn xn-1+a Fark Denkleminin Periyodikliği Üzerine

Yıl 2016, Cilt: 6 Sayı: 2, 329 - 333, 01.06.2016

Erkan Taşdemir Yüksel Soykan

https://doi.org/10.1155/2013/742912

Öz

Bu makalede, x-1 ve x0 başlangıç koşulları reel sayılar olmak üzere, n∈N0 için xn+1=xnxn-1+a, lineer olmayan fark denkleminin periyodikliği ve terimlerinin davranışları incelenmiştir

Anahtar Kelimeler

Sınırlılık Fark denklemleri Eninde sonunda periodiklik Periodiklik

Kaynakça

  • Amleh, AM., Camouzis, E., Ladas, G. 2008. On the dynamics of a rational difference equation, Part 2. IJDE, 3(2), 195-225.
  • Amleh, AM., Camouzis, E., Ladas, G. 2008. On the dynamics of a rational difference equation, Part I. IJDE, 3(1), 1-35.
  • Elaydi, S. 1996. An introduction to difference equations. New York: Springer.
  • Elsayed, EM., El-Dessoky, MM. 2013. Dynamics and global behavior for a fourth-order rational difference equation. Hacet. J. Math. Stat., 42(5), 479-494.
  • Gümüş, M. 2013. The Periodicity of Positive Solutions of the Nonlinear Difference Equation . Discrete Dyn. Nat. Soc., 2013, 1-3. doi:10.1155/2013/742912
  • Gümüş, M., Öcalan, Ö. 2012. Some Notes on the Difference Equation Discrete Dyn. Nat. Soc., 2012, 1-12. doi:10.1155/2012/258502
  • Gümüş, M., Öcalan, Ö. 2014. Global Asymptotic Stability of a Nonautonomous Difference Equation. J. Appl. Math., 2014, 1-5. doi:10.1155/2014/395954 x x2- 2x x2-x12-x2- 12-x12-x2- ax22
  • Öcalan, Ö., Ogünmez, H., Gümüş, M. 2014. Global behavior test for a nonlinear difference equation with a period-two coefficient. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 21(3-4), 307-316.
  • Stevic, S. 2008. On the difference equation . Comput. Math. Appl., 56, 1159-1171.
  • Stević, S. 2008. Nontrivial solutions of a higher-order rational difference equation. Math. Notes, 84(5-6), 718-724. doi:10.1134/s0001434608110138
  • Stević, S., Iričanin, B. 2011. Unbounded Solutions of the Difference Equation. Abstr. Appl. Anal., 2011, 1-8. doi:10.1155/2011/561682
  • Stević, S., Alghamdi, MA., Alotaibi, A. 2015. Boundedness character of the recursive sequence . Appl. Math. Lett., 50, 83- 90. doi:10.1016/j.aml.2015.06.006
  • Stevic, S., Diblik, J., Iricanin, B., Smarda, Z. 2014. Solvability of nonlinear difference equations of fourth order. EJDE, 2014(264), 1-14.

On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α

Yıl 2016, Cilt: 6 Sayı: 2, 329 - 333, 01.06.2016

Erkan Taşdemir Yüksel Soykan

https://doi.org/10.1155/2013/742912

Öz

In this paper, we investigate the periodicities and long-term behaviour of the nonlinear difference equation: , , where the initial conditions and are real numbers.

Anahtar Kelimeler

Difference Equations Boundedness Periodicity Eventual periodicity.

Kaynakça

  • Amleh, AM., Camouzis, E., Ladas, G. 2008. On the dynamics of a rational difference equation, Part 2. IJDE, 3(2), 195-225.
  • Amleh, AM., Camouzis, E., Ladas, G. 2008. On the dynamics of a rational difference equation, Part I. IJDE, 3(1), 1-35.
  • Elaydi, S. 1996. An introduction to difference equations. New York: Springer.
  • Elsayed, EM., El-Dessoky, MM. 2013. Dynamics and global behavior for a fourth-order rational difference equation. Hacet. J. Math. Stat., 42(5), 479-494.
  • Gümüş, M. 2013. The Periodicity of Positive Solutions of the Nonlinear Difference Equation . Discrete Dyn. Nat. Soc., 2013, 1-3. doi:10.1155/2013/742912
  • Gümüş, M., Öcalan, Ö. 2012. Some Notes on the Difference Equation Discrete Dyn. Nat. Soc., 2012, 1-12. doi:10.1155/2012/258502
  • Gümüş, M., Öcalan, Ö. 2014. Global Asymptotic Stability of a Nonautonomous Difference Equation. J. Appl. Math., 2014, 1-5. doi:10.1155/2014/395954 x x2- 2x x2-x12-x2- 12-x12-x2- ax22
  • Öcalan, Ö., Ogünmez, H., Gümüş, M. 2014. Global behavior test for a nonlinear difference equation with a period-two coefficient. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 21(3-4), 307-316.
  • Stevic, S. 2008. On the difference equation . Comput. Math. Appl., 56, 1159-1171.
  • Stević, S. 2008. Nontrivial solutions of a higher-order rational difference equation. Math. Notes, 84(5-6), 718-724. doi:10.1134/s0001434608110138
  • Stević, S., Iričanin, B. 2011. Unbounded Solutions of the Difference Equation. Abstr. Appl. Anal., 2011, 1-8. doi:10.1155/2011/561682
  • Stević, S., Alghamdi, MA., Alotaibi, A. 2015. Boundedness character of the recursive sequence . Appl. Math. Lett., 50, 83- 90. doi:10.1016/j.aml.2015.06.006
  • Stevic, S., Diblik, J., Iricanin, B., Smarda, Z. 2014. Solvability of nonlinear difference equations of fourth order. EJDE, 2014(264), 1-14.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Erkan Taşdemir

Yüksel Soykan Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

Kaynak Göster

APA Taşdemir, E., & Soykan, Y. (2016). On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α. Karaelmas Fen Ve Mühendislik Dergisi, 6(2), 329-333. https://doi.org/10.1155/2013/742912
AMA Taşdemir E, Soykan Y. On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α. Karaelmas Fen ve Mühendislik Dergisi. Haziran 2016;6(2):329-333. doi:10.1155/2013/742912
Chicago Taşdemir, Erkan, ve Yüksel Soykan. “On The Periodicies of The Difference Equation X_ n+1 =x_n X_ N-1 +α”. Karaelmas Fen Ve Mühendislik Dergisi 6, sy. 2 (Haziran 2016): 329-33. https://doi.org/10.1155/2013/742912.
EndNote Taşdemir E, Soykan Y (01 Haziran 2016) On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α. Karaelmas Fen ve Mühendislik Dergisi 6 2 329–333.
IEEE E. Taşdemir ve Y. Soykan, “On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α”, Karaelmas Fen ve Mühendislik Dergisi, c. 6, sy. 2, ss. 329–333, 2016, doi: 10.1155/2013/742912.
ISNAD Taşdemir, Erkan - Soykan, Yüksel. “On The Periodicies of The Difference Equation X_ n+1 =x_n X_ N-1 +α”. Karaelmas Fen ve Mühendislik Dergisi 6/2 (Haziran 2016), 329-333. https://doi.org/10.1155/2013/742912.
JAMA Taşdemir E, Soykan Y. On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α. Karaelmas Fen ve Mühendislik Dergisi. 2016;6:329–333.
MLA Taşdemir, Erkan ve Yüksel Soykan. “On The Periodicies of The Difference Equation X_ n+1 =x_n X_ N-1 +α”. Karaelmas Fen Ve Mühendislik Dergisi, c. 6, sy. 2, 2016, ss. 329-33, doi:10.1155/2013/742912.
Vancouver Taşdemir E, Soykan Y. On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α. Karaelmas Fen ve Mühendislik Dergisi. 2016;6(2):329-33.