Kathleen A. Hoffman


Predator Prey SystemsThe celebrated LotkaVolterra predatorprey system predicts oscillations in the populations. I analyzed an extension of the classical predatorprey 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 boundedpaired cascades to chaos. Subsequently, I have worked with master's student Nicole Massarelli to prove the HairstonSmithSlobodkin conjecture from ecology. Essentially the conjecture states for a chain of couple LotkaVolterra predatorprey equations, orbits for an even number of species are bounded, whereas orbits for an odd number of species are not bounded. 

Maintained by: Kathleen A. Hoffman
(khoffman@math.umbc.edu). 
