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Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator

Yıl 2019, Cilt: 11, 141 - 148, 30.12.2019

Öz

In this study, some necessary and sufficient conditions are given for the stability of linear delay difference equations involving generalized difference operator. For the root analysis Schur-Cohn criteria is used and some examples are given to verify the results.

Kaynakça

  • Agarwal, R.P., Difference Equations and Inequalities, Marcel Dekker, New York, 2000.
  • \v{C}erm\'{a}k, J., J\'{a}nsk\i , J.\ \& Kundr\'{a}t, P., \textit{On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations}, Journal of Difference Equations and Applications, \textbf{18(11)}(2011), 1781--1800.
  • Camouzis, E., Ladas, G., Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures, Chapman \&Hall, 2008.
  • Clark,C. W., \textit{A delay-recruitment model of populations dynamics with application to baleen whale populations}, J. Math. Biol., \textbf{3}(1976), 381--391.
  • Dannan, F.M., Elaydi, S., \textit{Asymptotic stability of linear difference equation of advanced type}, J. Comput. Anal. Appl., \textit{6}(2004), 173--187.
  • Elaydi, S., An Introduction to Difference Equations, 3nd ed., Springer, 2000.
  • Kelley, W.G., Peterson, A.C., Difference Equations. An Introduction with Applications, Academic Press inc, 1991.
  • Kuruklis, S.A., \textit{The asymptotic stability of x(n+1) - ax(n) +bx(n-k) = 0}, J. Math. Anal. Appl., \textbf{188}(1994), 719--731.
  • Levin, S., May, R., \textit{A note on difference-delay equations}, Theoretical Population Biol., \textbf{9}(1976), 178--187.
  • Liz, E., \textit{On explicit conditions for the asymptotic stability of linear higher order difference equations}, J. Math. Anal. Appl., \textbf{303}(2005), 492--498.
  • Matsunaga, H., Hara, T., \textit{The asymptotic stability of a two-dimensional linear delay difference equation}, Dynam. Contin. Discrete Impuls. Systems, \textbf{6}(1999), 465--473.
  • Matsunaga, H., Ogita, R., Murakami, K., \textit{Asymptotic behavior of a system of higher order linear difference equations}, Nonlinear Analysis, \textbf{47}(2001), 4667-4677.
  • Mickens, R.E., Difference Equations, Van Nostrand Reinhold Company, New York, 1990.
  • Popenda, J., Szmanda, B., \textit{On the oscillation of solutions of certain difference equations}, Demonstratio Mathematica, \textbf{XVII}(1984), 153--164.
  • Popenda, J., \textit{Oscillation and nonoscillation theorems for second-order difference equations}, J. Math. Anal. Appl., \textbf{123(1)}(1987), 34--38.
Yıl 2019, Cilt: 11, 141 - 148, 30.12.2019

Öz

Kaynakça

  • Agarwal, R.P., Difference Equations and Inequalities, Marcel Dekker, New York, 2000.
  • \v{C}erm\'{a}k, J., J\'{a}nsk\i , J.\ \& Kundr\'{a}t, P., \textit{On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations}, Journal of Difference Equations and Applications, \textbf{18(11)}(2011), 1781--1800.
  • Camouzis, E., Ladas, G., Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures, Chapman \&Hall, 2008.
  • Clark,C. W., \textit{A delay-recruitment model of populations dynamics with application to baleen whale populations}, J. Math. Biol., \textbf{3}(1976), 381--391.
  • Dannan, F.M., Elaydi, S., \textit{Asymptotic stability of linear difference equation of advanced type}, J. Comput. Anal. Appl., \textit{6}(2004), 173--187.
  • Elaydi, S., An Introduction to Difference Equations, 3nd ed., Springer, 2000.
  • Kelley, W.G., Peterson, A.C., Difference Equations. An Introduction with Applications, Academic Press inc, 1991.
  • Kuruklis, S.A., \textit{The asymptotic stability of x(n+1) - ax(n) +bx(n-k) = 0}, J. Math. Anal. Appl., \textbf{188}(1994), 719--731.
  • Levin, S., May, R., \textit{A note on difference-delay equations}, Theoretical Population Biol., \textbf{9}(1976), 178--187.
  • Liz, E., \textit{On explicit conditions for the asymptotic stability of linear higher order difference equations}, J. Math. Anal. Appl., \textbf{303}(2005), 492--498.
  • Matsunaga, H., Hara, T., \textit{The asymptotic stability of a two-dimensional linear delay difference equation}, Dynam. Contin. Discrete Impuls. Systems, \textbf{6}(1999), 465--473.
  • Matsunaga, H., Ogita, R., Murakami, K., \textit{Asymptotic behavior of a system of higher order linear difference equations}, Nonlinear Analysis, \textbf{47}(2001), 4667-4677.
  • Mickens, R.E., Difference Equations, Van Nostrand Reinhold Company, New York, 1990.
  • Popenda, J., Szmanda, B., \textit{On the oscillation of solutions of certain difference equations}, Demonstratio Mathematica, \textbf{XVII}(1984), 153--164.
  • Popenda, J., \textit{Oscillation and nonoscillation theorems for second-order difference equations}, J. Math. Anal. Appl., \textbf{123(1)}(1987), 34--38.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Murat Gevgeşoğlu 0000-0001-5215-427X

Yaşar Bolat 0000-0002-7978-1078

Yayımlanma Tarihi 30 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 11

Kaynak Göster

APA Gevgeşoğlu, M., & Bolat, Y. (2019). Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator. Turkish Journal of Mathematics and Computer Science, 11, 141-148.
AMA Gevgeşoğlu M, Bolat Y. Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator. TJMCS. Aralık 2019;11:141-148.
Chicago Gevgeşoğlu, Murat, ve Yaşar Bolat. “Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator”. Turkish Journal of Mathematics and Computer Science 11, Aralık (Aralık 2019): 141-48.
EndNote Gevgeşoğlu M, Bolat Y (01 Aralık 2019) Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator. Turkish Journal of Mathematics and Computer Science 11 141–148.
IEEE M. Gevgeşoğlu ve Y. Bolat, “Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator”, TJMCS, c. 11, ss. 141–148, 2019.
ISNAD Gevgeşoğlu, Murat - Bolat, Yaşar. “Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator”. Turkish Journal of Mathematics and Computer Science 11 (Aralık 2019), 141-148.
JAMA Gevgeşoğlu M, Bolat Y. Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator. TJMCS. 2019;11:141–148.
MLA Gevgeşoğlu, Murat ve Yaşar Bolat. “Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator”. Turkish Journal of Mathematics and Computer Science, c. 11, 2019, ss. 141-8.
Vancouver Gevgeşoğlu M, Bolat Y. Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator. TJMCS. 2019;11:141-8.