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 providin...
