Research Review:

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 deforming. My 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 as well.

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 intermittency.

Check out my list publications and preprints to get copies! Also here you can find more about my projects!
 

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