Stability of Equilibria in Quantitative Genetic Models Based on Modified-Gradient Systems

Authors

Benjamin J. Ridenhour, University of IdahoFollow
Jerry R. Ridenhour, Utah State UniversityFollow

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

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.

Recommended Citation

Benjamin J. Ridenhour & Jerry R. Ridenhour (2018) Stability of equilibria in quantitative genetic models based on modified-gradient systems, Journal of Biological Dynamics, 12:1, 39-50, DOI: 10.1080/17513758.2017.1400598