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Speaker: Glenn Ledder

Abstract:

1. I will discuss the general ideas behind the choice between discrete and continuous time for dynamical system models, illustrated by a comparison of two simple population models.
2. I will present a mixed-time (part discrete, part continuous) consumer-resource model that will serve as a further example of the points previously made.
3. I will present the key results of recently-published work on a mixed-time model for competition between consumers that builds on the mixed-time model of the second part of the talk.  Ecological theory predicts competitive exclusion; however, we will see that instability in the system of dominant-consumer-plus-resource can provide an opening that allows survival of the weaker competitor.  We will also see how dominance of one consumer over another can be modified by pulsed release of a toxin that affects one competitor more than the other.