Lecture 5
13 Maio 2020, 14:30 • Maria Teresa Faria da Paz Pereira
Presentation by a student: ``small delays are harmless"; study of the characteristic equations for some selected examples: a predator-prey model with two delays; a chemostat model with one discrete delay and stability of its equilibria; Nicholson blowflies’s equation.
Addenda to the predator prey model: conditions for the absolute (i.e., independently of the size of the delays) local asymptotic stability of the positive equilibrium.
Autonomous DDEs x'(t)=f(x_t) and semi-dynamical systems; (positive) orbits and omega-limit sets; if f is completely continuous, bounded positive orbits are pre-compact. Properties of the omega-limit sets.
This lecture took place on May 19, from 17h to 19h.