Bendixson's criterion for autonomous systems with an invariant linear subspace
The author studies the autonomous system \(x'= f(x)\) in \(\mathbb{R}^n\), with the hypothesis that the Jacobian matrix has the form \(- \nu I+ A(x)\). In addition, he assumes that there exists a constant matrix \(B\) such that \(BA(x)= 0\) for all \(x\) in the domain of the differential equation. He characterizes an invariant manifold of the system in terms of \(B\) and gives sufficient conditions for the nonexistence of invariant closed curves in the invariant manifold. An application to SEIS epidemic model is given.
scientific article; zbMATH DE number 796926