Ramazan ÇAKIROĞLU, Ahmet DUMAN, Kemal AYDIN

İkinci Mertebeden Fark Denklemlerin Hem Schur Kararlılığı Hem Salınımlılığı

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.

Anahtar Kelimeler:

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

On Schur Stability and Oscillation of Second Order Difference Equations

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,

PDF

___

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)