The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0
We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation xn+1-a2xn-1+bxn-k= 0, n=0, 1, ..., where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and...
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th-cmuir.6653943832-605582018-09-10T03:45:16Z The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 Piyapong Niamsup Yongwimon Lenbury Mathematics We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation xn+1-a2xn-1+bxn-k= 0, n=0, 1, ..., where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and b of difference equations. The method of proof is based on arithematic of complex numbers as well as properties of analytic functions. 2018-09-10T03:45:16Z 2018-09-10T03:45:16Z 2008-01-01 Journal 12256951 2-s2.0-77952124402 10.5666/KMJ.2008.48.2.173 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77952124402&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60558 |
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Mathematics |
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Mathematics Piyapong Niamsup Yongwimon Lenbury The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| description |
We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation xn+1-a2xn-1+bxn-k= 0, n=0, 1, ..., where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and b of difference equations. The method of proof is based on arithematic of complex numbers as well as properties of analytic functions. |
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Journal |
| author |
Piyapong Niamsup Yongwimon Lenbury |
| author_facet |
Piyapong Niamsup Yongwimon Lenbury |
| author_sort |
Piyapong Niamsup |
| title |
The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| title_short |
The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| title_full |
The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| title_fullStr |
The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| title_full_unstemmed |
The asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| title_sort |
asymptotic stability of x<inf>n+1</inf>-a<sup>2</sup>x<inf>n-1</inf>+bx<inf>n-k</inf>=0 |
| publishDate |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77952124402&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60558 |
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1681425457942102016 |