Showing papers on "Autonomous system (mathematics) published in 1972"
TL;DR: In this article, the authors deal with a now method developed for stability considerations of complicated linear or linearized systems with the aid of the eigenvalues of the system matrix, which is useful in cases where the stato variables have different dimensions.
Abstract: This paper deals with a now method developed for stability considerations of complicated linear or linearized systems with the aid of the eigenvalues of the system matrix. The method is useful in cases where the stato variables have different dimensions. One can then also get some information about the allowed region of the state variables, the autonomous system still remaining stable.
2 citations
TL;DR: In this paper, it was shown that (S) cannot have two weak foci nor a weak focus and a centre and conditions were obtained for the stability of the weak focus, and for the generation of a limit cycle by small perturbations which change a strong focus into a strong one.
Abstract: The cases of a strong (weak) focus or a centre are then examined in greater detail. It is shown, with the aid of results of Coppel [2], that (S) cannot have two weak foci nor a weak focus and a centre. Further, using the process of Poincare and Liapunov, conditions are obtained for the stability of the weak focus and for the generation of a limit cycle by small perturbations which change a weak focus into a strong one.