NVTB Symposium 30 Sept 2009

Application of bifurcation theory to population dynamics

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The morning program is in the aula, Vrije Universiteit (main building at de Boelelaan 1105) in Amsterdam

The afternoon program in room F619 of the Science-Building (de Boelelaan 1081) .

Morning Program on Wednesday 30 September 2009

09:30 Dirk Stiefs
Max Planck Institute for the Physics of Complex Systems Nöthnitzer Str. 38, D 01187 Dresden Germany
Relating generalized and specific modeling in population dynamical systems

09:30 welcome by Herman Verhoef (Rector Magnificus) in Aula
promotoren Bas Kooijman, Ulrike Feudel; copromotor Bob Kooi
09:30 Introduction by Dirk Stiefs
09:40 Prof. Dr. H. (Horst) Malchow
09:50 Prof. Dr. J. (Johan) Grasman
10:00 Dr. T. (Thilo) Gross
10:10 Dr. W. (Wolf) Mooij
10:20 Prof. Dr. J. (Jaap) van der Meer
10:30 end of defence

10:45 George van Voorn
dept Theoretical Biology, Vrije Universiteit, Amsterdam
Ecological implications of global bifurcations

10:45 welcome by Herman Verhoef (Rector Magnificus) in Aula
promotor Bas Kooijman; copromotoren Bob Kooi, Yuri Kuznetsov
10:45 Introduction by George van Voorn
10:55 Prof. Dr. U (Ulrike) Feudel
11:05 Prof. Dr. B. (Bernd) Krauskopf
11:15 Dr. M. (Martin) Boer
11:25 Prof Dr. H. (Horst) Malchow
11:35 Prof. Dr. J. (Jaap) van der Meer
11:45 end of defence; start of closed meeting
12:15 ceremony
12:30 end of ceremony

Dirk and George also have defended their theses succesfully in Oldenburg, Germany at 17 July 2009.

Afternoon Program on Wednesday 30 September 2009

Symposium sponsered by the NVTB
in room F619, W&N building (de Boelelaan 1081)

13:40 Coffee
13:50 Welcome by Bas Kooijman
14:00 Horst Malchow: Patterns of predation, competition and invasion in a noisy environment
14:30 Yuri Kuznetsov: Degenerate Bogdanov-Takens bifurcations in two and more dimensions
15:00 Tea
15:30 Ulrike Feudel: The interplay of hydrodynamics and plankton growth in the wake of an island
16:00 Bernd Krauskopf: Invariant manifolds in the Lorenz system

14:00 Horst Malchow
Professor in Theoretical Systems Science
Institute of Environmental Systems Research Department of Mathematics and Computer Science
University of Osnabrück, 49069 Osnabrück, Germany

Patterns of predation, competition and invasion in a noisy environment

The formation and spread of spatiotemporal structures in simple predation and competition-diffusion models is demonstrated. The analysis of the local systems yields a number of stationary and/or oscillatory regimes. Correspondingly interesting is the spatiotemporal behaviour, modelled by reaction-diffusion equations. Environmental fluctuations are modelled as parametric as well as external multiplicative noise, using stochastic partial differential equations. Noise can enhance the survival of a population that would go extinct in a deterministic environment. In the parameter range of excitability and slow-fast dynamics of prey and predator, respectively, noise can induce local and global oscillations as well as local coherence resonance, global synchronization and stationary spatial structures. The results are related to plankton dynamics, partly with viral infections of the prey population. Considering invasion in a fragmented habitat, it is shown that the variability of fragmentation as well as the mobilities of natives and invaders drive the invasion.

14:30 Yuri Kuznetsov
Associate Professor in Bifurcation Theory
Department of Mathematics, Utrecht University
Budapestlaan 6, 3584 CD Utrecht, The Netherlands

Degenerate Bogdanov-Takens bifurcations in two and more dimensions

Equilibria of ODEs with a double zero eigenvalue will be considered, when one of the coefficients of the classical Bogdanov normal form vanishes. A short summary of known results on bifurcations of phase portraits in generic planar cases will be given. Then the case of a "triple equilibrium with an elliptic sector" will be revisited. It will be shown numerically that this case is unexpectedly similar to the much better studied "triple focus case", and give a planar ODE describing the two-stage (juvenile-adult) age-structured population dynamics, where a transition between the focus case and the elliptic case occurs. Explicit formulas for the critical coefficients of the degenerate BT normal form will be presented, which are valid for two- and more dimensional systems. The algorithm will be illustrated on with a prey-predator system by Bazykin.

15:30 Ulrike Feudel
Professor in Theoretical Physics/Complex Systems
Institut für Chemie und Biologie des Meeres
Carl von Ossietzky Universität Oldenburg
PF 2503, D-26111 Oldenburg, Germany

The interplay of hydrodynamics and plankton growth in the wake of an island

Plankton patterns as observed in satellite images of the ocean are a result of the interaction of population dynamics with physical transport processes. We study the planktonic biological activity in the wake of an island which is close to an upwelling region providing nutrients for the growth of the plankton. Our results are based on the numerical analysis of a simple kinematic flow mimicking the hydrodynamics in the wake coupled to a three component plankton model. We show that the mesoscale hydrodynamic structures can under certain conditions either act as a barrier blocking the transport of nutrients or facilitating transport of nutrients leading to an enhanced primary production. In particular we show that in a special case mesoscale vortices act as incubators for plankton growth leading to localized plankton blooms within vortices in the wake of an island. The mechanism of the emergence of these localized plankton blooms relies on the intricate interplay of hydrodynamic and biological time scales. Furthermore we show that mesoscale hydrodynamic structures play an important role for dominance patterns of competing species.

16:00 Bernd Krauskopf
Professor of Applied Nonlinear Mathematics
Department of Engineering Mathematics University of Bristol
Queen's Building, Bristol BS8 1TR, United Kingdom

Invariant manifolds in the Lorenz system

This talk will discuss how the stable manifold of the origin of the Lorenz system interacts with the unstable manifolds of secondary equilibria and bifurcating saddle periodic orbits.

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