Harvesting in diffusive population models (Cont'd) 


, denotes the
population growth rate,
for describes the
efforts of crowding,
represents a constant yield
harvesting rate, and
is the initial population. Here, reflects the
harvesting quota (a humanly controllable factor)
and
reflects the
intrinsic properties of the region.
We assume that for all
. The
Dirichlet
condition
on the
boundary refers to a
hostile
boundary, and the Neumann condition
on
corresponds
to the case of no migration through the
boundary. The functions and are assumed
continuous on , and is assumed to
be piecewise
continuous on .
We certainly do not expect the
REU students to analyze the above
problems as stated. Their involvement in mathematical research will
mostly be in the onedimensional case. However, some of their
computational analysis will include the twodimensional case.
The students will learn the importance of sensitivity analysis
as well as the stability and asymptotic properties of the solutions
to these models and their relevance in population dynamics.
Such an experience will surely inspire them to more advanced research,
at a later stage, combining both mathematical analysis and
computational simulations.
The 20032005 NSF REU students at MSU achieved great success on
this research. We are confident that this research topic will
be highly successful again with the 20092011 NSF REU students.
