Optimal Control of an Invasive Species in Competition
A paper on this subject was published by the >Journal of Biological Dynamics in the fall of 2007 (follow the link or go to the Papers and Reprints link in the menu). Links to collaborators are available on the links page.
This work presents an ode model for population interactions between an
invasive and a native species, where the effect of disturbance in the
system (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 us to consider
quadratic growth functions of 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.
Upcoming work in this area includes consideration of a spatial-temporal
optimal control for a PDE model.