MR2381324
Hongshan REN
Hongshan REN
Stability Analysis of Second Order Delay Difference Equations
Funkcialaj Ekvacioj. Serio Internacia
50
2007
405--419
http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-3/50_405.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2381324
In this paper, we will give a necessary and sufficient condition for the zero solution of second order delay difference equations of the form<br />
$x_{n+2}-ax_n+bx_{n-k}=0, n=0, 1, 2, \cdots,$<br />
to be asymptotically stable, which is easy to verify and to apply, where $a$ and $b$ are non-zero real constants, $k$ is a positive integer.
Delay difference equation, Asymptotic stability, Characteristic equation.
39A10, 39A11.
50-405
2007
Stability Analysis of Second Order Delay Difference Equations
Hongshan REN
Hongshan REN
1
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The Asymptotic Stability of $x_{n+1}-ax_n+bx_{n-k}=0$
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1994
719-731
MR1305480
2
Dannan, F. M.
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2004
589-599
MR2060414