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ON THE STABILITY OF A THIRD ORDER DIFFERENCE EQUATION

Year 2020, , 132 - 141, 31.12.2020
https://doi.org/10.34186/klujes.795061

Abstract

Bu çalışmada x_(n+1)=x_(n-1) x_(n-2)+A fark denkleminin A pozitif bir reel sayı ve başlangıç koşulları pozitif iken denge noktaları incelendi. Ayrıca ilgili fark denkleminin lokal asimptotik kararlılığı çalışıldı. Özellikle ilgili denklemin çözümlerinin yakınsaklığı incelendi.



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References

  • Agarwal, R. P. and Wong, P. J., Advanced topics in difference equations (Vol. 404), Springer Science & Business Media, 2013.
  • Amleh, A. M., Camouzis, E. and Ladas, G., On the Dynamics of a Rational Difference Equation Part 1, Int. J. Difference Equ., vol. 3, no. 1, pp. 1-35, 2008.
  • Camouzis, E. and Ladas, G., Dynamics of third order rational difference equations with open problems and conjectures, volume 5 of Advances in Discrete Mathematics and Applications, Chapman & Hall/CRC, Boca Raton, 2008.
  • Elaydi, S., An Introduction to Difference Equations, Springer-Verlag, New York, 1996.
  • Kent, C. M. and Kosmala, W., On the Nature of Solutions of the Difference Equation , International Journal of Nonlinear Analysis and Applications, vol. 2, no. 2, pp. 24-43, 2011.
  • Kent, C. M., Kosmala, W., Radin, M. A. and Stevic, S., Solutions of the difference equation , Abstr. Appl. Anal., vol. 2010, pp. 1-13, 2010.
  • Kent, C. M., Kosmala, W. and Stevic, S., Long-term behavior of solutions of the difference equation , Abstr. Appl. Anal., vol. 2010, pp. 1-17, 2010.
  • Kent, C. M., Kosmala, W. and Stevic, S., On the difference equation , Abstr. Appl. Anal., vol. 2011, pp. 1-15, 2011.
  • Kulenovic, M. R. S. and Ladas, G., Dynamics of second order rational difference equations with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, FL, 2002.
  • Liu, K., Li, P., Han, F. and Zhong, W., Behavior of the Difference Equations J. Comput. Anal. Appl., vol. 22, no. 1, pp. 1361-1370, 2017.
  • Okumuş, İ., Soykan, Y., Dynamical behavior of a system of three-dimensional nonlinear difference equations, Adv. Difference Equ., vol. 2018, no. 224, pp. 1-15, 2018.
  • Stevic, S. and Iričanin, B., Unbounded solutions of the difference equation Abstr. Appl. Anal., vol. 2011, pp. 1-8, 2011.
  • Taşdemir, E., On the Asymptotically Periodic Solutions of A Fifth Order Difference Equation, J. Math. Anal. vol. 10, no. 3, pp. 100-111, 2019.
  • Taşdemir, E., On The Dynamics of a Nonlinear Difference Equation, Adıyaman University Journal of Science, vol. 9, no. 1, pp. 190-201, 2019.
  • Taşdemir, E. and Soykan, Y., On the Periodicies of the Difference Equation Karaelmas Science and Engineering Journal, vol. 6, no. 2, pp. 329-333, 2016.
  • Taşdemir, E. and Soykan, Y., Long-Term Behavior of Solutions of the Non-Linear Difference Equation Gen. Math. Notes, vol. 38, no. 1, pp. 13-31, 2017.
  • Taşdemir, E. and Soykan, Y., Stability of Negative Equilibrium of a Non-Linear Difference Equation, J. Math. Sci. Adv. Appl., vol. 49, no. 1, pp. 51-57, 2018.
  • Taşdemir, E. and Soykan, Y., Dynamical Analysis of a Non-Linear Difference Equation, J. Comput. Anal. Appl., vol. 26, no. 2, pp. 288-301, 2019.
  • Wang, Y., Luo, Y., Lu, Z., Convergence of solutions of Appl. Math. E-Notes, vol. 12, pp. 153-157, 2012.

ON THE STABILITY OF A THIRD ORDER DIFFERENCE EQUATION

Year 2020, , 132 - 141, 31.12.2020
https://doi.org/10.34186/klujes.795061

Abstract

In this paper, we are investigated the equilibrium points of difference equation x_(n+1)=x_(n-1) x_(n-2)+A, where A is a positive real number and the initial conditions are positive. We are also studied the local asymptotic stability of related difference equation. Particularly, we are examined the convergence of solutions of related equation.



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References

  • Agarwal, R. P. and Wong, P. J., Advanced topics in difference equations (Vol. 404), Springer Science & Business Media, 2013.
  • Amleh, A. M., Camouzis, E. and Ladas, G., On the Dynamics of a Rational Difference Equation Part 1, Int. J. Difference Equ., vol. 3, no. 1, pp. 1-35, 2008.
  • Camouzis, E. and Ladas, G., Dynamics of third order rational difference equations with open problems and conjectures, volume 5 of Advances in Discrete Mathematics and Applications, Chapman & Hall/CRC, Boca Raton, 2008.
  • Elaydi, S., An Introduction to Difference Equations, Springer-Verlag, New York, 1996.
  • Kent, C. M. and Kosmala, W., On the Nature of Solutions of the Difference Equation , International Journal of Nonlinear Analysis and Applications, vol. 2, no. 2, pp. 24-43, 2011.
  • Kent, C. M., Kosmala, W., Radin, M. A. and Stevic, S., Solutions of the difference equation , Abstr. Appl. Anal., vol. 2010, pp. 1-13, 2010.
  • Kent, C. M., Kosmala, W. and Stevic, S., Long-term behavior of solutions of the difference equation , Abstr. Appl. Anal., vol. 2010, pp. 1-17, 2010.
  • Kent, C. M., Kosmala, W. and Stevic, S., On the difference equation , Abstr. Appl. Anal., vol. 2011, pp. 1-15, 2011.
  • Kulenovic, M. R. S. and Ladas, G., Dynamics of second order rational difference equations with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, FL, 2002.
  • Liu, K., Li, P., Han, F. and Zhong, W., Behavior of the Difference Equations J. Comput. Anal. Appl., vol. 22, no. 1, pp. 1361-1370, 2017.
  • Okumuş, İ., Soykan, Y., Dynamical behavior of a system of three-dimensional nonlinear difference equations, Adv. Difference Equ., vol. 2018, no. 224, pp. 1-15, 2018.
  • Stevic, S. and Iričanin, B., Unbounded solutions of the difference equation Abstr. Appl. Anal., vol. 2011, pp. 1-8, 2011.
  • Taşdemir, E., On the Asymptotically Periodic Solutions of A Fifth Order Difference Equation, J. Math. Anal. vol. 10, no. 3, pp. 100-111, 2019.
  • Taşdemir, E., On The Dynamics of a Nonlinear Difference Equation, Adıyaman University Journal of Science, vol. 9, no. 1, pp. 190-201, 2019.
  • Taşdemir, E. and Soykan, Y., On the Periodicies of the Difference Equation Karaelmas Science and Engineering Journal, vol. 6, no. 2, pp. 329-333, 2016.
  • Taşdemir, E. and Soykan, Y., Long-Term Behavior of Solutions of the Non-Linear Difference Equation Gen. Math. Notes, vol. 38, no. 1, pp. 13-31, 2017.
  • Taşdemir, E. and Soykan, Y., Stability of Negative Equilibrium of a Non-Linear Difference Equation, J. Math. Sci. Adv. Appl., vol. 49, no. 1, pp. 51-57, 2018.
  • Taşdemir, E. and Soykan, Y., Dynamical Analysis of a Non-Linear Difference Equation, J. Comput. Anal. Appl., vol. 26, no. 2, pp. 288-301, 2019.
  • Wang, Y., Luo, Y., Lu, Z., Convergence of solutions of Appl. Math. E-Notes, vol. 12, pp. 153-157, 2012.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Issue
Authors

Erkan Taşdemir 0000-0002-5002-3193

Tülin Erdoğan Taşdemir This is me 0000-0002-7333-0217

Publication Date December 31, 2020
Published in Issue Year 2020

Cite

APA Taşdemir, E., & Erdoğan Taşdemir, T. (2020). ON THE STABILITY OF A THIRD ORDER DIFFERENCE EQUATION. Kirklareli University Journal of Engineering and Science, 6(2), 132-141. https://doi.org/10.34186/klujes.795061