Lecture 5

4 Dezembro 2017, 15:30 • Maria Teresa Faria da Paz Pereira

Characteristic equations for linear autonomous DDEs (cont.) and applications: 1. The logistic equation (or Wright's equation) with one discrete delay and the equation x'(t)=-ax(t-r) revisited. 2. The linear DDE x′(t) = Ax(t) + Bx(t − r) (r > 0), where A,B are nxn matrices; the particular case of scalar equations (n=1) and sharp conditions for the asymptotic stability. 3. A predator-prey model with two delays and conditions for the absolute (i.e., independently of the size of the delays) local asymptotic stability of the positive equilibrium. 4. A chemostat model with one discrete delay and stability of its equilibria.(
(This class took place on Wednesday Dec. 6, from 18h to 19h45.)