| Kathleen A. Hoffman
The celebrated Lotka-Volterra predator-prey system predicts
oscillations in the populations. I analyzed an extension of the
classical predator-prey equations that include an omnivore, a third
species that is a predator of the prey and scavenges the carcasses of
the predator and proved that the systems has bounded orbits, and for
certain parameter values, exhibits bounded-paired cascades to chaos.
Subsequently, I have worked with master's student
to prove the Hairston-Smith-Slobodkin
conjecture from ecology. Essentially the conjecture states for a chain
of couple Lotka-Volterra predator-prey equations, orbits for an even
number of species are bounded, whereas orbits for an odd number of
species are not bounded.