Apr. 13th 2004 
Prof. Dr.
Martin Hasler Swiss Fed. Inst. of Technology, Lausanne 
Complete synchronization of regular and smallworld networks of dynamical systems 
Diffusively coupled dynamical systems with arbitrary coupling graphs are
considered. Explicit upper bounds for the minimal coupling strength
(diffusion constant) needed to achieve complete synchronization are derived
using Lyapunov functions in the difference variables. These bounds are a
product of a term depending only on the individual system dynamics and a
term depending only on the coupling graph. The latter is formulated purely
in graph theoretical terms. Furthermore, systems where all or part of the
couplings are switched on and off in a random fashion are considered. It is
proved that for sufficiently fast switching, complete synchronization is
almost always achieved, if the averaged system completely synchronizes. This
is applied to smallworld networks where in addition to fixed couplings
"shortcut" couplings are switched on and off. It is shown that even with
very low probability of switching shortcuts on, the coupling strength
needed to achieve complete synchronization can be considerably lowered.

Apr. 20th 2004
3:45 p.m. 
Prof. Dr.
Arnd Scheel University of Minnesota, Minneapolis 
Corner defects in interface propagation 
We study existence and stability of curved interfaces in planar
reactiondiffusion systems.
We start with a planar, xindependent front and investigate the
existence of traveling waves which locally resemble the primary front.
The problem of existence of corners is reduced to an ordinary
differential equation that can be viewed as the travellingwave equation
to a viscous conservation law or variants of the KuramotoSivashinsky
equation.
The corner typically but not always points in the direction opposite
to the direction of propagation.
For the existence and stability problem, we rely on a spatial dynamics
formulation with an appropriate equivariant parameterization for
relative equilibria.
We also comment on oscillatory front propagation, invasion of patterns,
and viscous shock waves in anisotropic systems.

Apr. 27th 2004
2:00 p.m. 
Festkolloquium zu Ehren von Klaus Schneider
WIAS Berlin, 10117 Berlin, Mohrenstr. 39,
ErhardSchmidtHörsaal

 14:00 Reiner Lauterbach (Universität Hamburg)
 Symbolic computations in equivariant problems
 14:45 Bernold Fiedler (Freie Universität Berlin)
 Rotating spirals of curvature flows: a center manifold example
 15:30 Kaffeepause
 16:00 Jan Sieber (University of Bristol)
 Dynamics of piecewise smooth delay equations
 16:45 N.N. Nefedov (Staatl. LomonossovUniversität Moskau)
 Generation and propagation of fronts in IVP with periodic nonlinearity

May 11th 2004 
Dr.
Dmitrii Rachinskii WIASBerlin 
Sector estimates in Hopf bifurcation problems 
May 18th 2004
2:30 p.m. 
Prof. Dr. Leonid Cherkas Minsk, State
University 
Limit cycles of polynomial vector fields 
WIAS Berlin, 10117 Berlin, Mohrenstr. 39,
ErhardSchmidtHörsaal

May 25th 2004 
Prof. Dr. Dan Luss University of Houston 
Temperature patterns in catalytic reactors 
June 8th 2004 
Dr. Jens Rademacher
University of Minnesota 
Homoclinic orbits near heteroclinic cycles with periodic orbits 
New results on homoclinic orbits near certain generic
codimension1 and 2 heteroclinic cycles between an equilibrium and a
periodic orbit are presented. In the codimension2 case the global
topology of heteroclinic sets determines the number of curves of
homoclinic orbits
that bifurcate and influences the leading order expansion of parameter
curves.
The codimension1 case partially explains the phenomenon of 'tracefiring' in
reactiondiffusion equations, which is the bifurcation of a stable
excitation pulse to a selfreplicating pulsechain. For the Oregonator
model the codimension2 case can be used to understand the loss of
stability of the primary pulse.

June 22nd 2004 
Dr. Sarah Day Cornell University 
Conley index techniques for global dynamics: a
study of the SwiftHohenberg equation 
June 29nd 2004 
Prof. Mohamed Belhaq
Univ. Hassan II, Casablanca 
Fast Vibrations in Mechanical Systems 
July 6th 2004 
Prof. Dmitry Turaev
University of Ber Sheva, Israel 
On maps close to identity 