Asymptotic Stability of Linear Delay Difference Equations Including Generalized Difference Operator
Yıl 2019,
Cilt: 11, 141 - 148, 30.12.2019
Murat Gevgeşoğlu
Yaşar Bolat
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
Murat Gevgeşoğlu
Yaşar Bolat
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.