Verschiedene Dozenten: Population Dynamics Day 2012
Wednesday, 04.07.2012 14:15 im Raum M5
Prof. Dr. Odo Diekmann, Utrecht University
A delay equation is a rule for extending a function of time towards the
future, on the basis of the known past. Renewal Equations prescribe the
current value, while Delay Differential Equations prescribe the
derivative of the current value. With a delay equation one can associate
a dynamical system by translation along the extended function.
I will illustrate by way of examples how such equations arise in the
description of the dynamics of structured populations and sketch the
available theory, while making a plea for the development of numerical
bifurcation tools.
The lecture is based on joint work with Mats Gyllenberg, Hans Metz and
many others.
The spectral radius of a positive operator: eigenvectors,
bounds, and approximation by power methods
Horst R. Thieme, Arizona State University
In structured population models,
the basic reproduction number often is the spectral radius of an appropriate
positive linear operator on an ordered Banach space.
This operator is called next generation operator in case
a biological interpretation is available. Since a closed expression
for its spectral radius can only be obtained in special cases,
there is renewed interest in the approximation and estimation of the
spectral radius.
Quite a few results are available in the operator theory and
computational/numerical literature. It is one of the purposes
of this talk to review
some of these and perhaps give them a new twist.
Motivated by two-sex population models, we extend our study to
homogeneous increasing maps on cones. We present conditions for
convergence of iterates to balanced geometric growth (strong ergodicity)
and for convergence of power methods to the cone spectral radius and the
associated eigenvector.
Anlagen
Poster PDD3.pdf
Angelegt am 16.04.2012 von Carolin Gietz
Geändert am 20.11.2012 von Frank Wübbeling
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