My research focuses mainly in finite and infinite dimensional dynamical
systems applied to physical systems. I have been working on new mechanism
of transition to chaos. These deal with degenerate objects which are found
in the phase space of dynamical systems, and are known as homoclinic and
heteroclinic orbits. These are one responsible for transition to chaos
to many systems, but now more complicated scenarios have been studied.
For this we studied system which do not involve a spatial dimension and
may be modelled by ordinary differential equations, and others where spatial
dimension is important, and have been studied by reaction-diffusion equations.
In the latter we investigated the dynamics of coherent structures, which
are localized objects in space which travel through the medium without
doctorate thesis illustrates some
physical applications where the above can be found. I have been working
with lasers and catalysis on a Pt surface.The main idea was to focus on
degerate bifurcations which in fact organized the whole relevant
bifurcation diagram of the system.
Work in the area of complex adaptive systems
is in progress. This goes from analysing a very simple society,
used to model artificial societies. The main subject has been "Cooperation",
and we studied a model using the Prisoners Dilemma in a random network.
We have studied how cooperation can arise whenever agents are allowed to
change partners, thus the network of connections was allowed to evolve.
Also another application of evolving networks is that of a finantial
market model. We have studied how the herding effect may account part of
the large probability of large returns in a stock value. The model is an
evolving percolation type model, which may be interesting for other applications
I am currently interested in stochastic system. What are the
tools to understand the dynamics of a stochastic system? Stationary probability
distributions are clearly not enough to recover dynamics. How can we extract
dynamical information out of a stochastic system? We have modeled spatio-temporal
intermittency via a stochastic extended system. Our main contribution was
to show how the nucleation of a metastable state may develop as spatio-temporal
Check out my list publications and preprints
to get copies! Also here you can find more about my projects!
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