Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 4 Sayı: 2, 89 - 102, 31.08.2021
https://doi.org/10.33187/jmsm.929981

Öz

Kaynakça

  • [1] Mickens RE. Difference Equations. Van Nostrand Reinhold Comp: New York, 1987.
  • [2] Mackey MC, Glass L. Oscillation and chaos in physiological control system. Science 1977; 197:287–289.
  • [3] Kulenovic MRS, Ladas G. Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall / CRC Press, 2001.
  • [4] V.L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
  • [5] R. Agarwal, Difference equations and inequalities. Theory, methods and applications, Marcel Dekker Inc., New York, 1992.
  • [6] H. Chen and H. Wang, Global attractivity of the difference equation $x_{n+1}=\dfrac{x_{n}+\alpha x_{n-1}}{\beta +x_{n}}$, Appl. Math. Comp., 181 (2006) 1431–1438.
  • [7] C. Cinar, On the positive solutions of the difference equation $ x_{n+1}=\dfrac{ax_{n-1}}{1+bx_{n}x_{n-1}},$, Appl. Math. Comp., 156 (2004) 587-590.
  • [8] S. E. Das and M.Bayram, On a System of Rational Difference Equations, World Applied Sciences Journal 10(11) (2010), 1306-1312.
  • [9] Q. Din, and E. M. Elsayed, Stability analysis of a discrete ecological model, Computational Ecology and Software 4 (2) (2014), 89–103.
  • [10] Beverton RJ, Holt SJ. On the Dynamics of Exploited Fish Populations, Vol. 19. Fish Invest.: London, 1957.
  • [11] DeVault R, Dial G, Kocic V. L, Ladas G. Global behavior of solutions of $x_{n+1}=ax_{n}+f(x_{n},\ x_{n-1})$. Journal of Difference Equations and Applications 1997, 3(3-4), 311–330.
  • [12] E. M. Elabbasy, H. El-Metwally and E. M. Elsayed, On the difference equations$x_{n+1}=\dfrac{\alpha x_{n-k}}{\beta +\gamma \prod_{i=0}^{k}x_{n-i}},$, J. Conc. Appl. Math., 5(2) (2007), 101-113.
  • [13] E. M. Elabbasy, H. El-Metwally and E. M. Elsayed, Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33 (4) (2007), 861-873.
  • [14] E. M. Elabbasy, H. El-Metwally and E. M. Elsayed, On the Difference Equation $x_{n+1}=\frac{a_{0}x_{n}+a_{1}x_{n-1}+...+a_{k}x_{n-k}}{% b_{0}x_{n}+b_{1}x_{n-1}+...+b_{k}x_{n-k}}$, Mathematica Bohemica, 133 (2) (2008), 133-147.
  • [15] E.M. Elsayed, Qualitative behaviour of difference equation of order two Mathematical and Computer Modelling 50 (2009) 1130 1141.
  • [16] Elabbasy and E. M. Elsayed, On the difference equation, $x_{n+1}=\frac{.\alpha x_{n-l}+\beta x_{n-k}}{Ax_{n-l}+Bx_{n-k}},$, Acta Mathematica Vietnamica, 33 (2008), 85–94.

Dynamics and Expression of Solution of a Sixth Order Difference Equation

Yıl 2021, Cilt: 4 Sayı: 2, 89 - 102, 31.08.2021
https://doi.org/10.33187/jmsm.929981

Öz

This paper deals with the solution behavior and periodic nature of the solutions of the difference equation $$ s_{n+1}=\alpha s_{n}+\dfrac{\beta s_{n}s_{n-4}}{\gamma s_{n-4}+\delta s_{n-5} },\;\;\;n=0,1,... $$ {\Large \noindent }where the initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1},\ s_{0}$ are arbitrary positive real numbers and $\alpha ,\ \beta ,\ \gamma ,\ \delta \ $are positive constants. Also we obtain the closed form of the solutions of some special cases of this equation.

Kaynakça

  • [1] Mickens RE. Difference Equations. Van Nostrand Reinhold Comp: New York, 1987.
  • [2] Mackey MC, Glass L. Oscillation and chaos in physiological control system. Science 1977; 197:287–289.
  • [3] Kulenovic MRS, Ladas G. Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall / CRC Press, 2001.
  • [4] V.L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
  • [5] R. Agarwal, Difference equations and inequalities. Theory, methods and applications, Marcel Dekker Inc., New York, 1992.
  • [6] H. Chen and H. Wang, Global attractivity of the difference equation $x_{n+1}=\dfrac{x_{n}+\alpha x_{n-1}}{\beta +x_{n}}$, Appl. Math. Comp., 181 (2006) 1431–1438.
  • [7] C. Cinar, On the positive solutions of the difference equation $ x_{n+1}=\dfrac{ax_{n-1}}{1+bx_{n}x_{n-1}},$, Appl. Math. Comp., 156 (2004) 587-590.
  • [8] S. E. Das and M.Bayram, On a System of Rational Difference Equations, World Applied Sciences Journal 10(11) (2010), 1306-1312.
  • [9] Q. Din, and E. M. Elsayed, Stability analysis of a discrete ecological model, Computational Ecology and Software 4 (2) (2014), 89–103.
  • [10] Beverton RJ, Holt SJ. On the Dynamics of Exploited Fish Populations, Vol. 19. Fish Invest.: London, 1957.
  • [11] DeVault R, Dial G, Kocic V. L, Ladas G. Global behavior of solutions of $x_{n+1}=ax_{n}+f(x_{n},\ x_{n-1})$. Journal of Difference Equations and Applications 1997, 3(3-4), 311–330.
  • [12] E. M. Elabbasy, H. El-Metwally and E. M. Elsayed, On the difference equations$x_{n+1}=\dfrac{\alpha x_{n-k}}{\beta +\gamma \prod_{i=0}^{k}x_{n-i}},$, J. Conc. Appl. Math., 5(2) (2007), 101-113.
  • [13] E. M. Elabbasy, H. El-Metwally and E. M. Elsayed, Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33 (4) (2007), 861-873.
  • [14] E. M. Elabbasy, H. El-Metwally and E. M. Elsayed, On the Difference Equation $x_{n+1}=\frac{a_{0}x_{n}+a_{1}x_{n-1}+...+a_{k}x_{n-k}}{% b_{0}x_{n}+b_{1}x_{n-1}+...+b_{k}x_{n-k}}$, Mathematica Bohemica, 133 (2) (2008), 133-147.
  • [15] E.M. Elsayed, Qualitative behaviour of difference equation of order two Mathematical and Computer Modelling 50 (2009) 1130 1141.
  • [16] Elabbasy and E. M. Elsayed, On the difference equation, $x_{n+1}=\frac{.\alpha x_{n-l}+\beta x_{n-k}}{Ax_{n-l}+Bx_{n-k}},$, Acta Mathematica Vietnamica, 33 (2008), 85–94.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Abdul Khaliq 0000-0001-8802-9200

Yayımlanma Tarihi 31 Ağustos 2021
Gönderilme Tarihi 29 Nisan 2021
Kabul Tarihi 10 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 2

Kaynak Göster

APA Khaliq, A. (2021). Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of Mathematical Sciences and Modelling, 4(2), 89-102. https://doi.org/10.33187/jmsm.929981
AMA Khaliq A. Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of Mathematical Sciences and Modelling. Ağustos 2021;4(2):89-102. doi:10.33187/jmsm.929981
Chicago Khaliq, Abdul. “Dynamics and Expression of Solution of a Sixth Order Difference Equation”. Journal of Mathematical Sciences and Modelling 4, sy. 2 (Ağustos 2021): 89-102. https://doi.org/10.33187/jmsm.929981.
EndNote Khaliq A (01 Ağustos 2021) Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of Mathematical Sciences and Modelling 4 2 89–102.
IEEE A. Khaliq, “Dynamics and Expression of Solution of a Sixth Order Difference Equation”, Journal of Mathematical Sciences and Modelling, c. 4, sy. 2, ss. 89–102, 2021, doi: 10.33187/jmsm.929981.
ISNAD Khaliq, Abdul. “Dynamics and Expression of Solution of a Sixth Order Difference Equation”. Journal of Mathematical Sciences and Modelling 4/2 (Ağustos 2021), 89-102. https://doi.org/10.33187/jmsm.929981.
JAMA Khaliq A. Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of Mathematical Sciences and Modelling. 2021;4:89–102.
MLA Khaliq, Abdul. “Dynamics and Expression of Solution of a Sixth Order Difference Equation”. Journal of Mathematical Sciences and Modelling, c. 4, sy. 2, 2021, ss. 89-102, doi:10.33187/jmsm.929981.
Vancouver Khaliq A. Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of Mathematical Sciences and Modelling. 2021;4(2):89-102.

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