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Full-Text Articles in Physical Sciences and Mathematics
Stability Of Equilibria In Quantitative Genetic Models Based On Modified-Gradient Systems, Benjamin J. Ridenhour, Jerry R. Ridenhour
Stability Of Equilibria In Quantitative Genetic Models Based On Modified-Gradient Systems, Benjamin J. Ridenhour, Jerry R. Ridenhour
Mathematics and Statistics Faculty Publications
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.
Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo
Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo
Mathematics and Statistics Faculty Publications
Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, …