A Qualitative Analysis of X ̇=Ax+b

Author

Terry Lynn Bone, Missouri University of Science and TechnologyFollow
Clark Jeffries
Victor Klee

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