Event Detail

Event Type: 
Analysis Seminar
Date/Time: 
Monday, November 20, 2017 - 12:00 to 13:00
Location: 
Gilkey 104

Speaker Info

Local Speaker: 
Abstract: 

Many microbial populations exhibit social behavior, e.g. by producing enzymes required to digest the nutrients needed for growth. Unfortunately, this provides opportunities for "cheaters" to invade these populations. Cheaters let others produce the enzyme, and only invest in their own growth. In a previous talk, I showed that when cheaters appear, the entire population is doomed. This phenomenon is known as the Tragedy of the Commons (ToC). In this talk, we will examine which mechanisms prevent this tragedy. This will be achieved by analyzing the global dynamics of a system of 5 nonlinear ODEs which can be reduced to a 3-dimensional competitive system. A powerful Poincare-Bendixson theory is available for this class of systems,
which makes a global asymptotic analysis feasible in ways comparable to planar systems.