DYNAMICAL SYSTEM SEMINAR
Place: Room SE 215, Math building, Florida Atlantic University.
Time: 3pm
Thursday, September 10th 2009th: 3.00 pm
Rob VANDERVORST (FAU-Math dept/Vrije Universiteit Amsterdam)
Title:
Braids & Dynamics
Abstract:
We study the non-autonomous Hamilton equations in the plane.
The extended phase space of such a system
is 3-dimensional and the orbits
may display all kinds of knotting and braiding.
We use the topology of braids to construct solutions
of the Hamilton equations.
This way forcing results (does a given solution
force additional solutions?) are obtained.
We mention also applications to area-preserving maps.
Thursday, September 24th 2009th: 2.40 pm
Armin FUCHS (Center for Complex Systems and Brain Sciences)
Title:
Structure, Dynamics and Function of the Human Brain: Noninvasive Recording
Techniques and Realistic Models.
Abstract: Starting from the question: what are the basic requirements to describe and understand a complex system, we give an overview on the modern noninvasive imaging techniques that provide insight into the human brain.s structure and function. We discuss the effects that homogeneous (short-range) and heterogeneous (long-range) connections within the system have on its dynamical behavior based on simple models that include transmission delays. Finally, we show how the folded cortical surface can be incorporated in realistic models of structure, dynamics and function of the human brain.
Thursday, October 8th 2009th: 3.00 pm
Emmanuelle TOGNOLI (Center for Complex Systems and Brain Sciences)
Title:
Reading the mysterious language of the brain: a dynamical challenge for
the next decade
Abstract:
Understanding nature's law, whether in simple manifestations or in
complexity, requires a human mind to grasp and interpret patterns and
regularities. These patterns can be mapped onto different systems of the
human mind: numbers, geometries, equations, words, images, symbols, etc...
On all counts, the human brain is a complex system, and it poses so many
challenges that some thinkers questioned whether it could ever understand
itself. Rather than avoiding this inherent paradox, we embraced it and
enquired about the brain that understands prior to asking about the brain
to be understood. Brain function can be framed as a spatio-temporal
problem. Its neurons are fixed and functionally arranged as a result of
philogeny and ontogeny. Its activity is ever-changing in time, and I will
show how distinctly ephemeral are brain functional patterns as compared to
those from systems that loose or lack complexity.
For the typical human observer, space and time are perceived as different
currencies of nature. Our recent efforts went into exposing brain activity
in time and cortical surface simultaneously; a 4-dimensional space at the
very least. Natural human perception could not be relied upon; it is
bounded to a maximum of 3-dimensions. To circumvent this ceiling, the
trick was to understand how order emerges from the human mind and to
reroute spatial and temporal information to perceptual channels that could
run in concert. It gave rise to a 4-dimensional colorimetric visualization
of spatio-temporal data. The technique opened up the possibility to read
functional states of the brain from continuous records of its activity;
and also to come to grip with testing theories of brain self-organization.
The upcoming challenge is to decipher the mysterious language of the brain
and maybe someday to establish fundamental laws of the human minds.
Thursday, October 22th 2009th: 3.00 pm
SPECIAL SEMINAR: Ram MOHAPATRA (Central Florida
University)
Title: On Epidemiological models with mutating pathogens
Abstract: In this talk we shall discuss some epidemiological models for
the transmission of a pathogen that can mutate
in a host to create a second infectious
mutant strain. Explicit formulas for the reproductive
number on an epidemic based on the local
stability of the infection-free equilibrium will
be mentioned. We shall also analyze the
existence and stability of the boundary equilibrium and
the endemic equilibrium. We shall talk about
the global stability of the boundary equilibrium.
Finally we shall show that under certain circumstances
there is Hopf bifurcation where the endemic equilibrium
loses its stability, and periodic solutions appear.
Some numerical simulations to illustrate Hopf bifurcation
will be considered. Finally recent results on application of Homotopy
Analysis Method to epidemiological models will be mentioned.
Thursday, October 29th 2009th: 2.50 pm
Robert ROUSSARIE (Institut Mathematiques de Bourgogne)
Title:
Bifurcation Theory For Planar Vector Fields
Abstract: In contrast
with the situation
in higher
dimensions, a bifurcation theory for multi-parameter families of vector fields was developed in
dimension 2 until some point, especially on the plane.
First, I want to recall
some basic notions as for instance what
is a versal unfolding and make precise the
ultimate goal for the theory:
that is to obtain all possible
versal unfoldings and to find a
good description of generic k-parameter
families in terms of these versal unfoldings.
Next I shall review some important results
obtained up to now and
I shall also mention some open questions.
Finally I shall give an idea about the methods we use:
normal forms, rescaling and desingularization, asymptotics.
Thursday, November 19th 2009th: 3 pm
Silke DODEL (Center for Complex Systems and Brain Sciences)
Title: Objective dynamical measures of team coordination and performance
Abstract: team is more than just a group of people.
But how can team
coordination and
performance be measured?
A team consisting
of one excellent and several poor members may score
reasonably well by conventional standards, but may not in terms of team coordination.
We developed novel measures of team performance and team coordination that overcome
limitations of current team performance measures, such as being subjective and
ignoring
dynamic team processes. By using concepts from theoretical physics and
dynamical systems theory we represent team dynamics geometrically as a manifold.
The deviation of the actual team trajectory from the optimal manifold provides an
objective measure of team performance, while the direction of the deviation informs
about the nature of the performance
deficiency. By expanding this approach we in addition assess the evolution of team coordination over
time, both for the team as a whole and for all pairs of individual team members to reveal dynamic
coordination patterns in teams.