Apr. 13th 2004 |
Prof. Dr.
Martin Hasler Swiss Fed. Inst. of Technology, Lausanne |
Complete synchronization of regular and small-world 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 small-world networks where in addition to fixed couplings
"short-cut" couplings are switched on and off. It is shown that even with
very low probability of switching short-cuts 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
reaction-diffusion systems.
We start with a planar, x-independent 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 travelling-wave equation
to a viscous conservation law or variants of the Kuramoto-Sivashinsky
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,
Erhard-Schmidt-Hörsaal
|
- 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. Lomonossov-Universität Moskau)
- Generation and propagation of fronts in IVP with periodic nonlinearity
|
May 11th 2004 |
Dr.
Dmitrii Rachinskii WIAS-Berlin |
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,
Erhard-Schmidt-Hörsaal
|
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
codimension-1 and -2 heteroclinic cycles between an equilibrium and a
periodic orbit are presented. In the codimension-2 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 codimension-1 case partially explains the phenomenon of 'tracefiring' in
reaction-diffusion equations, which is the bifurcation of a stable
excitation pulse to a self-replicating pulse-chain. For the Oregonator
model the codimension-2 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 Swift-Hohenberg 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 |
Talks usually take place on Tuesday at 3:15 p.m.
at the Free University Berlin, Department of Mathematics/Computer science
in room 108/109, Arnimallee 6 (the "Pi-Building"), 14195 Berlin.
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !