A qualitative analysis of \(\dot x=Ax+b\)
For a dynamical system \(\dot x=Ax+b\), where A is a constant real \(n\times n\) matrix and b is an n-vector, there is special interest in the existence of a constant asymptotically stable attractor trajectory in the positive orthant of \({\mathbb{R}}^ n\). 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 nonlinear systems and ecosystem models are also mentioned.
constant asymptotically stable attractor trajectory
scientific article; zbMATH DE number 4054107
scientific article