A Qualitative Analysis of X ̇=Ax+b
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.
T. L. Bone et al., "A Qualitative Analysis of X ̇=Ax+b," Discrete Applied Mathematics, Elsevier, May 1988.
The definitive version is available at http://dx.doi.org/10.1016/0166-218X(88)90038-8
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© 1988 Elsevier, All rights reserved.