Research Article
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İkinci Mertebeden Fark Denklemlerin Hem Schur Kararlılığı Hem Salınımlılığı

Year 2021, Volume: 11 Issue: 4, 3098 - 3110, 15.12.2021

Ramazan Çakıroğlu Ahmet Duman , Kemal Aydın

https://doi.org/10.21597/jist.902856

Abstract

Bu çalışmada, ikinci mertebeden fark denklemlerinin çözümlerinin davranışı üzerine sonuçlar incelenmiştir. Çözümün hangi pertürbeler altında karakteristik özelliklerini koruduğunu belirleyen sonuçlar verildi. Elde edilen sonuçlar nümerik örnekler ile incelendi.

Keywords

Fark denklemleri Schur kararlılık Hurwitz kararlılık salınımlılık hassasiyet bozunum sistemleri şart sayısı

References

  • Agarwal RP, 2000. Difference equations and inequalities. Marcel Dekker. New York.
  • Akın Ö, Bulgak H, 1998. Linear difference equations and stability theory. Selçuk University Research Centre of Applied Mathhematics. Konya. (Turkish).
  • Asteris PG, Chatzarakis GE, 2017. Oscillation tests for difference equations with non-monotone arguments. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 24(4): 287−302.
  • Braverman E, Karpuz B, 2011. On oscillation of differential and difference equations with non-monotone delays. Appl. Math. Comput. 218: 3880– 3887.
  • Chatzarakis GE, Shaikhet L, 2017. Oscillation criteria for difference equations with non-monotone arguments. Adv. Difference Equ. 62: 16pages.
  • Daganzo CF, 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B. 28(4): 269-287.
  • Duman A, Aydın K, 2011. Sensitivity of Schur stability of monodromy matrix. Applied Mathematics and Computation 217: 6663–6670.
  • Duman A, Aydın K, 2011. Sensitivity of Schur stability of systems of linear difference equations with constant coefficients. Scientific Research and Essays 6(28): 5846–5854.
  • Duman A, Aydın K, 2014. Some results on the sensitivity of Schur stability of linear difference equations with constant coefficients. Konuralp Journal of Mathematics 2(2): 22–34.
  • Duman A, Çelik GK, Aydın K, 2016. Sensitivity of Schur stability of systems of linear difference equations with periodic coefficients. New Trends in Mathematical Sciences 4(2): 159-173.
  • Duman A, Çelik GK, Aydın K, 2018. Sensitivity of Schur Stability of the k-th Order difference Equation System . Konuralp Journal of Mathematics 6(1): 7-13.
  • Elaydi SN, Sacker RJ, 2005. Global stability of periodic orbits of non-autonomous difference equations and population biology. Journal of Differential Equations 208(1): 258–273.
  • Elaydi SN, 2005. An introduction to difference equations. Springer. New York.
  • Györi I, Ladas G, 1991. Oscillation theory of delay differential equations. Clarendon press. Oxford.
  • Neusser K, 2019. Difference equations for economist. http://neusser.ch/downloads/Difference Equations.pdf. (Accessed 11 November 2020)

On Schur Stability and Oscillation of Second Order Difference Equations

Year 2021, Volume: 11 Issue: 4, 3098 - 3110, 15.12.2021

Ramazan Çakıroğlu Ahmet Duman , Kemal Aydın

https://doi.org/10.21597/jist.902856

Abstract

In this study, the results on the behavior of the solutions of second order difference equations are examined. The results determining under which perturbation the solutions retain their characteristics are given. The obtained results are analyzed with numerical examples.

Keywords

Difference equations Schur stability Hurwitz stability oscillation sensitivity perturbation systems condition number

References

  • Agarwal RP, 2000. Difference equations and inequalities. Marcel Dekker. New York.
  • Akın Ö, Bulgak H, 1998. Linear difference equations and stability theory. Selçuk University Research Centre of Applied Mathhematics. Konya. (Turkish).
  • Asteris PG, Chatzarakis GE, 2017. Oscillation tests for difference equations with non-monotone arguments. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 24(4): 287−302.
  • Braverman E, Karpuz B, 2011. On oscillation of differential and difference equations with non-monotone delays. Appl. Math. Comput. 218: 3880– 3887.
  • Chatzarakis GE, Shaikhet L, 2017. Oscillation criteria for difference equations with non-monotone arguments. Adv. Difference Equ. 62: 16pages.
  • Daganzo CF, 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B. 28(4): 269-287.
  • Duman A, Aydın K, 2011. Sensitivity of Schur stability of monodromy matrix. Applied Mathematics and Computation 217: 6663–6670.
  • Duman A, Aydın K, 2011. Sensitivity of Schur stability of systems of linear difference equations with constant coefficients. Scientific Research and Essays 6(28): 5846–5854.
  • Duman A, Aydın K, 2014. Some results on the sensitivity of Schur stability of linear difference equations with constant coefficients. Konuralp Journal of Mathematics 2(2): 22–34.
  • Duman A, Çelik GK, Aydın K, 2016. Sensitivity of Schur stability of systems of linear difference equations with periodic coefficients. New Trends in Mathematical Sciences 4(2): 159-173.
  • Duman A, Çelik GK, Aydın K, 2018. Sensitivity of Schur Stability of the k-th Order difference Equation System . Konuralp Journal of Mathematics 6(1): 7-13.
  • Elaydi SN, Sacker RJ, 2005. Global stability of periodic orbits of non-autonomous difference equations and population biology. Journal of Differential Equations 208(1): 258–273.
  • Elaydi SN, 2005. An introduction to difference equations. Springer. New York.
  • Györi I, Ladas G, 1991. Oscillation theory of delay differential equations. Clarendon press. Oxford.
  • Neusser K, 2019. Difference equations for economist. http://neusser.ch/downloads/Difference Equations.pdf. (Accessed 11 November 2020)
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Ramazan Çakıroğlu This is me 0000-0001-9242-9784

Ahmet Duman 0000-0002-4022-5285

Kemal Aydın 0000-0002-5843-3058

Publication Date December 15, 2021
Submission Date March 25, 2021
Acceptance Date July 3, 2021
Published in Issue Year 2021 Volume: 11 Issue: 4

Cite

APA Çakıroğlu, R., Duman, A., & Aydın, K. (2021). On Schur Stability and Oscillation of Second Order Difference Equations. Journal of the Institute of Science and Technology, 11(4), 3098-3110. https://doi.org/10.21597/jist.902856
AMA Çakıroğlu R, Duman A, Aydın K. On Schur Stability and Oscillation of Second Order Difference Equations. J. Inst. Sci. and Tech. December 2021;11(4):3098-3110. doi:10.21597/jist.902856
Chicago Çakıroğlu, Ramazan, Ahmet Duman, and Kemal Aydın. “On Schur Stability and Oscillation of Second Order Difference Equations”. Journal of the Institute of Science and Technology 11, no. 4 (December 2021): 3098-3110. https://doi.org/10.21597/jist.902856.
EndNote Çakıroğlu R, Duman A, Aydın K (December 1, 2021) On Schur Stability and Oscillation of Second Order Difference Equations. Journal of the Institute of Science and Technology 11 4 3098–3110.
IEEE R. Çakıroğlu, A. Duman, and K. Aydın, “On Schur Stability and Oscillation of Second Order Difference Equations”, J. Inst. Sci. and Tech., vol. 11, no. 4, pp. 3098–3110, 2021, doi: 10.21597/jist.902856.
ISNAD Çakıroğlu, Ramazan et al. “On Schur Stability and Oscillation of Second Order Difference Equations”. Journal of the Institute of Science and Technology 11/4 (December 2021), 3098-3110. https://doi.org/10.21597/jist.902856.
JAMA Çakıroğlu R, Duman A, Aydın K. On Schur Stability and Oscillation of Second Order Difference Equations. J. Inst. Sci. and Tech. 2021;11:3098–3110.
MLA Çakıroğlu, Ramazan et al. “On Schur Stability and Oscillation of Second Order Difference Equations”. Journal of the Institute of Science and Technology, vol. 11, no. 4, 2021, pp. 3098-10, doi:10.21597/jist.902856.
Vancouver Çakıroğlu R, Duman A, Aydın K. On Schur Stability and Oscillation of Second Order Difference Equations. J. Inst. Sci. and Tech. 2021;11(4):3098-110.