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Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri

Year 2018, Volume: 8 Issue: 2, 585 - 589, 01.06.2018

Abstract

Bu makalede negatif olmayan A, B, C, p1 ,p2 parametreleri ve negatif olmayan xxx - - 2 1 , , 0 başlangıç koşulları için x , , ,... B Cx x Ax n n 0 1 n p n p n 1 1 2 = 1 2 + + = - - lineer olmayan fark denkleminin global dinamiklerini araştıracağız. 2010 AMS-Konu Sınıflandırılması: 39A10, 39A20

References

  • Ahmed, AM. 2011. On the dynamics of a higher-order rational difference equation, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 419789, 8 pages.
  • Chen, D., Li, X. 2012. Some dynamical properties for a class of nonlinear difference equation, ADMS, 1(2), 1-12.
  • Chen, D., Li, X., Wang, Y. 2009. Dynamics for non-linear difference equation xn1= in Difference Equations, Volume 2009, Article ID 235691, 13 pages. ,n= 0 1
  • ...,Advances B Cxn s- + +n1n
  • Camouzis, E., Ladas, G. 2007. Dynamics of third-order rational difference equations with open problems and conjectures, Vol. 5. CRC Press.
  • El-Owaidy, HM., Ahmed, AM., Youssef, AM. 2005. The dynamics of the recursive sequence xn1= Axn1/B Cxn,2, + App. Math. Let., 18(9): 1013-1018. k/B Cxn, -/B Cxn,2, +n1n -,2
  • Elsayed, EM. 2014. New method to obtain periodic solutions of period two and three of a rational difference equation. Nonlinear Dyn., 79(1): 241-250.
  • Erdogan, ME., Cinar, C. 2013. On the dynamics of the recur- =Axn1/BB+Ct sive sequence xn+ Fasciculi Math., 50: 59-66. xnk2- p xni2- q k %i1=1== 1n+ -/BB+Ct aB+Ct/k1=1== k.
  • Gocen, M., Cebeci, A. 2018. On the periodic solutions of some systems of higher order difference equations, Rocky Mountain Journal of Mathematics, 48(3): 845-858.
  • Gocen, M., Guneysu, M. 2018. The global attractivity of some rational difference equations. Journal of Comput. Anal. and App., 25(7): 1233-1243.
  • Karatas, R. 2010. Global behavior of a higher order difference equation, Comput. Math. App., 60(3): 830-839.
  • Kocić, V., Ladas, G. 1993. Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht.
  • Kulenović, MRS., Ladas, G. 2001. Dynamics of second order rational difference equations, Chapman & Hall/CRC.
  • Sedaghat, H. 2003. Nonlinear difference equations theory with applications to social science models, Vol. 15. Springer Science & Business Media.
  • Tasdemir, E., Soykan, Y. 2016. On The Periodicies of The Difference Equation x(n+1)=xnx(n-1)+α. Karaelmas Fen ve Mühendislik Dergisi, 6(2): 329-333.
  • Tasdemir, E., Soykan, Y. 2019. Dynamical analysis of a non- linear difference equation. Journal of Comput. Anal. & App., 26(2): 288-301.
  • Tasdemir, E., Soykan, Y. 2017. Long-Term Behavior of Solutions of the Non-Linear Difference Equation xn+1=xn− 1xn−3−1. Gen. Math. Notes, 38(1): 13-31.

Global Dynamics of a Third-Order Rational Difference Equation

Year 2018, Volume: 8 Issue: 2, 585 - 589, 01.06.2018

Abstract

In this paper, we will investigate the global dynamics of the following non-linear difference equation x , , ,... B Cx x Ax n n 0 1 n p n p n 1 1 2 = 1 2 + + = - - where the parameters A, B, C, p1 ,p2 are non-negative numbers and the initial values xxx - - 2 1 , , 0 are non-negative numbers. 2010 AMS-Mathematical Subject Classification Number: 39A10, 39A20

References

  • Ahmed, AM. 2011. On the dynamics of a higher-order rational difference equation, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 419789, 8 pages.
  • Chen, D., Li, X. 2012. Some dynamical properties for a class of nonlinear difference equation, ADMS, 1(2), 1-12.
  • Chen, D., Li, X., Wang, Y. 2009. Dynamics for non-linear difference equation xn1= in Difference Equations, Volume 2009, Article ID 235691, 13 pages. ,n= 0 1
  • ...,Advances B Cxn s- + +n1n
  • Camouzis, E., Ladas, G. 2007. Dynamics of third-order rational difference equations with open problems and conjectures, Vol. 5. CRC Press.
  • El-Owaidy, HM., Ahmed, AM., Youssef, AM. 2005. The dynamics of the recursive sequence xn1= Axn1/B Cxn,2, + App. Math. Let., 18(9): 1013-1018. k/B Cxn, -/B Cxn,2, +n1n -,2
  • Elsayed, EM. 2014. New method to obtain periodic solutions of period two and three of a rational difference equation. Nonlinear Dyn., 79(1): 241-250.
  • Erdogan, ME., Cinar, C. 2013. On the dynamics of the recur- =Axn1/BB+Ct sive sequence xn+ Fasciculi Math., 50: 59-66. xnk2- p xni2- q k %i1=1== 1n+ -/BB+Ct aB+Ct/k1=1== k.
  • Gocen, M., Cebeci, A. 2018. On the periodic solutions of some systems of higher order difference equations, Rocky Mountain Journal of Mathematics, 48(3): 845-858.
  • Gocen, M., Guneysu, M. 2018. The global attractivity of some rational difference equations. Journal of Comput. Anal. and App., 25(7): 1233-1243.
  • Karatas, R. 2010. Global behavior of a higher order difference equation, Comput. Math. App., 60(3): 830-839.
  • Kocić, V., Ladas, G. 1993. Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht.
  • Kulenović, MRS., Ladas, G. 2001. Dynamics of second order rational difference equations, Chapman & Hall/CRC.
  • Sedaghat, H. 2003. Nonlinear difference equations theory with applications to social science models, Vol. 15. Springer Science & Business Media.
  • Tasdemir, E., Soykan, Y. 2016. On The Periodicies of The Difference Equation x(n+1)=xnx(n-1)+α. Karaelmas Fen ve Mühendislik Dergisi, 6(2): 329-333.
  • Tasdemir, E., Soykan, Y. 2019. Dynamical analysis of a non- linear difference equation. Journal of Comput. Anal. & App., 26(2): 288-301.
  • Tasdemir, E., Soykan, Y. 2017. Long-Term Behavior of Solutions of the Non-Linear Difference Equation xn+1=xn− 1xn−3−1. Gen. Math. Notes, 38(1): 13-31.
There are 17 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Mehmet Gümüş This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

Cite

APA Gümüş, M. (2018). Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri. Karaelmas Fen Ve Mühendislik Dergisi, 8(2), 585-589.
AMA Gümüş M. Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri. Karaelmas Fen ve Mühendislik Dergisi. June 2018;8(2):585-589.
Chicago Gümüş, Mehmet. “Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri”. Karaelmas Fen Ve Mühendislik Dergisi 8, no. 2 (June 2018): 585-89.
EndNote Gümüş M (June 1, 2018) Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri. Karaelmas Fen ve Mühendislik Dergisi 8 2 585–589.
IEEE M. Gümüş, “Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri”, Karaelmas Fen ve Mühendislik Dergisi, vol. 8, no. 2, pp. 585–589, 2018.
ISNAD Gümüş, Mehmet. “Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri”. Karaelmas Fen ve Mühendislik Dergisi 8/2 (June 2018), 585-589.
JAMA Gümüş M. Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri. Karaelmas Fen ve Mühendislik Dergisi. 2018;8:585–589.
MLA Gümüş, Mehmet. “Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 8, no. 2, 2018, pp. 585-9.
Vancouver Gümüş M. Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri. Karaelmas Fen ve Mühendislik Dergisi. 2018;8(2):585-9.