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

Erkan Taşdemir; Yüksel Soykan

doi:10.1155/2013/742912

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

Year 2016, Volume: 6 Issue: 2, 329 - 333, 01.06.2016

Erkan Taşdemir Yüksel Soykan

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

Abstract

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

Keywords

Sınırlılık, Fark denklemleri, Eninde sonunda periodiklik, Periodiklik

References

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

Year 2016, Volume: 6 Issue: 2, 329 - 333, 01.06.2016

Erkan Taşdemir Yüksel Soykan

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

Abstract

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

Keywords

Difference Equations, Boundedness, Periodicity, Eventual periodicity.

References

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.

There are 13 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	Erkan Taşdemir Yüksel Soykan This is me
Publication Date	June 1, 2016
Published in Issue	Year 2016 Volume: 6 Issue: 2

Cite

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. June 2016;6(2):329-333. doi:10.1155/2013/742912
Chicago	Taşdemir, Erkan, and Yüksel Soykan. “On The Periodicies of The Difference Equation X_ n+1 =x_n X_ N-1 +α”. Karaelmas Fen Ve Mühendislik Dergisi 6, no. 2 (June 2016): 329-33. https://doi.org/10.1155/2013/742912.
EndNote	Taşdemir E, Soykan Y (June 1, 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 and Y. Soykan, “On The Periodicies of The Difference Equation x_ n+1 =x_n x_ n-1 +α”, Karaelmas Fen ve Mühendislik Dergisi, vol. 6, no. 2, pp. 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 (June 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 and Yüksel Soykan. “On The Periodicies of The Difference Equation X_ n+1 =x_n X_ N-1 +α”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 6, no. 2, 2016, pp. 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.