- Project Background:
Some insect species are able to time their emergence from the larval
stage so that a very large number of individuals appear at the same
time.
Pine bark beetles and cicadas do this.
It is believed that fitness is enhanced by emerging en masse.
Larger numbers of insects may be able to overcome the defenses of
vegetation that are resistant to small numbers of insects.
Having a large number of potential mates improves the chances of
leaving offspring in the next generation.
There may also be safety in numbers from predators when a large
population of identical insects emerges simultaneously.
Biologists have a theory that this synchronized emergence is related
to environmental temperature.
When yearly average temperature deviates from normal, the yearly cycle
of emergence can be broken.
- Project Description:
The student will develop and analyze a mathematical model of an insect
population which exhibits synchronized emergence.
The student will study the mathematical models of insect populations
and circle maps.
The dynamical concept of the rotation number of a circle map may aid
in the development and the analysis of the model.
- Desired Student Background:
Ability to program in a high-level language, preferably Mathematica, C/C++,
and mathematical knowledge at the
level of MATH 365 Ordinary Differential Equations.