Instability of discrete systems
In this paper, we give criteria for instability and asymptotic instability for the null solution to the non-autonomous system of difference equations $$ y(t+1)=A(t)y(t) + f(t,y(t)),quad f(t,0)=0,, $$ when the system $x(t+1)=A(t)x(t)$ is unstable. In particular for $A$ constant, we study instability...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
1998-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1998/33/abstr.html |
| Summary: | In this paper, we give criteria for instability and asymptotic instability for the null solution to the non-autonomous system of difference equations $$ y(t+1)=A(t)y(t) + f(t,y(t)),quad f(t,0)=0,, $$ when the system $x(t+1)=A(t)x(t)$ is unstable. In particular for $A$ constant, we study instability from a new point of view. Our results are obtained using the method of discrete dichotomies, and cover a class of difference systems for which instability properties cannot be deduced from the classical results by Perron and Coppel. |
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| ISSN: | 1072-6691 |