Kathleen A. Hoffman

Predator Prey Systems

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 Nicole Massarelli 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.

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