Abstract:
Global
compact attractors, in combination with Lyapunov functions and the
Laplace transform, can be used to prove the global stability of
extinction and persistence equilibria. A linearized stability analysis
can be bypassed. For illustration, two models are considered:
one for bacteria and phages in a chemostat;
and one for the spread of an infection in a spatially distributed population.
References:
Hal L. Smith, Horst R. Thieme,
Dynamical Systems and Population Persistence, AMS, to appear 2011
Hal. L. Smith, Horst R. Thieme,
Persistence of bacteria and phages in a chemostat, preprint
Horst R. Thieme,
Global stability of the endemic equilibrium in
infinite dimension: Lyapunov functions and positive operators, preprint