Document Type

Article

Journal/Book Title/Conference

Journal of Biological Dynamics

Volume

12

Issue

1

Publisher

Taylor & Francis

Publication Date

11-20-2017

First Page

39

Last Page

50

DOI

https://doi.org/10.1080/17513758.2017.1400598

Abstract

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system x′ = P(t)∇f(x) which arise as critical points of f, under the assumption that P(t) is positive semi-definite. It is shown that the condition ∫λ1(P(t)) dt = ∞, where λ1(P(t)) is the smallest eigenvalue of P(t), plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.

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