Üçüncü Mertebeden Rasyonel Bir Fark Denkleminin Global Dinamikleri

Yıl 2018, Cilt: 8 Sayı: 2, 585 - 589, 01.06.2018

Mehmet Gümüş

Öz

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

Anahtar Kelimeler

Fark denklem, Denge noktası, Global kararlılık, Tekrarlı dizi

Global Dynamics of a Third-Order Rational Difference Equation

Öz

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

Anahtar Kelimeler

Difference equation, Global stability, Recursive sequence, Equilibrium point

Kaynakça

• 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.