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arXiv · 1608.04423

Stability of Equilibria in Modified-Gradient Systems

Benjamin J. Ridenhour·Jerry R. Ridenhour
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Abstract

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system $\mathbf{x}^{\prime}=P(t)\nabla f(x)$ which arise as critical points of $f$, under the assumption that $P(t)$ is positive semi-definite. It is shown that the condition $\int^{\infty}\lambda_{1}(P(t))~dt=\infty$, where $\lambda_{1}(P(t))$ 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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BibTeXRIS

Benjamin J. Ridenhour, Jerry R. Ridenhour. 2016-08-15. Stability of Equilibria in Modified-Gradient Systems. https://arxiv.org/abs/1608.04423

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