Mathematics and its Applications Seminar
Daniel Kern
Florida Gulf Coast University
Competing Populations and Optimized Disturbance
Abstract: I will present a model for population interactions between an
invasive and a native species, where the effect of disturbance in the
systems (such as flooding) is modeled as a control variable in the
growth terms. The motivating example is cottonwood-salt cedar
competition, with flooding being detrimental at low and high levels
and being advantageous at medium levels, which led to quadratic
growth functions in the control. An objective functional is
formulated to maximize the native species while minimizing the cost
of implementing the control. A new existence result for an optimal
control with these quadratic growth functions is given. Numerical
results are examined for various parameter values. The results
provide suggestions for managing the disturbance regime when invasive
species are present.
Wednesday March 3, 2010 at 4:00 PM in SEO 636