MATH DEPARTMENT COLLOQUIUM
4:00-5:00 PM Friday in 115 Avery
SPEAKER: Martin Bohner, University of Missouri-Rolla
Hosted by: Al Peterson
TITLE: Recent Results for Dynamic Equations on Time Scales
ABSTRACT: We give a brief introduction to the theory of dynamic
equations on time scales. Then we proceed to present and verify the
Cushing-Henson conjectures on time scales. The central part of these
conjectures asserts that based on a model using the dynamic
Beverton-Holt equation, a periodic environment is deleterious for the
population. The proof technique is as follows: First, the
Beverton-Holt equation is identified as a logistic dynamic equation.
The usual substitution transforms this equation into a linear
equation. Then the proof is completed using a recently established
dynamic version of the generalized Jensen inequality. If time permits,
we also will consider the case of harvesting with constant effort and
will maximize the seasonal sustainable yield to find the optimal
harvesting policy and the optimal population level. The main objects
in this talk are logistic differential equations, logistic difference
equations, and their unified counterparts, logistic dynamic equations
on time scales.
