Stefan Ericsson

Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model.

A discrete model for a metapopulation consisting of two local populations connected by migration is described and analyzed. It is assumed that the local populations grow according to the logistic law, that both populations have the same emigration rate, and that migrants choose their new habitat patch at random. Mathematically this leads to a coupled system of two logistic equations. A complete characterization of fixed point and two-periodic orbits is given, and a bifurcation analysis is performed. The region in the parameter plane where the diagonal is a global attractor is determined. In the symmetric case, where both populations have the same growth rate, the analysis is rigorous with complete proofs. In the nonsymmetric case, where the populations grow at different rates, the results are obtained numerically. The results are interpreted biologically. Particular attention is given to the sense in which migration has a stabilizing and synchronizing effect on local dynamics.

An Analysis Method for Sampling in Shift-Invariant Spaces

A subspace V of L2(ℝ) is called shift-invariant if it is the closed linear span of integer-shifted copies of a single function. As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method to derive both new results and relatively simple proofs of some previously known results. Among these are some results of rather general nature and some more specialized results for B-spline wavelets. The main problem under study is to find a shift x0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x0 + k + δk))k∈ℤ, either when all δk = 0 or in the irregular sampling case with an upper bound supk|δk| < δ.

IRREGULAR SAMPLING IN SHIFT INVARIANT SPACES OF HIGHER DIMENSIONS

We consider irregular sampling in shift invariant spaces V of higher dimensions. The problem that we address is: find e so that given perturbations (λk) satisfying sup|λk| < e, we can reconstruct an arbitrary function f of V as a Riesz basis expansions from its irregular sample values f(k + λk). A framework for dealing with this problem is outlined and in which one can explicitly calculate sufficient limits e for the reconstruction. We show how it works in two concrete situations.