A Qualitative Analysis of X ̇=Ax+b
Abstract
For a dynamical system x ̇=Ax+b, where A is constant real n×n matrix and b is an n-vector there is special interest in the existence of a constant asymptotically stable attractor trajectory in positive orthant of Rn. For certain patterns of signs of entries (+, -, or 0) in A and b, such a trajectory always must exist, regardless of the magnitudes of those entries. This paper describes all such patterns in terms of digraphs. Applications to a nonlinear systems and ecosystem models are also mentioned. © 1988.
Recommended Citation
T. L. Bone et al., "A Qualitative Analysis of X ̇=Ax+b," Discrete Applied Mathematics, Elsevier, May 1988.
The definitive version is available at https://doi.org/10.1016/0166-218X(88)90038-8
Department(s)
Chemistry
International Standard Serial Number (ISSN)
0166-218X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 1988 Elsevier, All rights reserved.
Publication Date
01 May 1988
