Research groups UPC Dinamical Systems (UPCDS)

UPC Dinamical Systems (UPCDS)

The research activity of the UPCDS group focuses on the development of analytical and numerical methods for dynamic systems, enjoying scientific leadership in several areas such as integrability, KAM theory, Arnold diffusion, splitting of separatrices, exponentially small phenomena, as well as applications to celestial mechanics, astrodynamics and neuroscience.

The value of this activity is reflected in the quality and quantity of publications, some of them in collaboration with leading international groups, as well as in the implication of the group in different scientific events (conferences and seminars, research programs, thematic networks (DANCE), etc.), and in various editorial boards of prestigious journals. The group has also a large training experience organizing advanced schools like the JISD and supervising full doctoral training.

Main projects

  • 1.

    Dynamics Associated to Connections between Invariant objects with Applications to Neuroscience and Astrodynamics

    This project belongs to the area of Dynamical Systems and Applications, focusing on the local study and, mainly, the global study of continuous and discrete dynamical systems using analytical and numerical tools. The goal of the project consists on keep our leadership in the areas of Arnold Diffusion, splitting of separatrices and Astrodynamics, as well as advance in the study of bifurcations, computation of invariant objects and integrability. But we also want to strengthen the application of Dynamical Systems tools to problems in Astrodynamics, Celestial Mechanics, Chemistry and, as was most recently done with great success, in infinite dimensional Dynamical Systems and Neuroscience. In order to obtain numerical results not only in some theoretical problems, like exponentially small splitting of separatrices, but also in applications to Astrodynamics, Celestial Mechanics or Neuroscience, a highly computational approach is necessary, and very often it is only possible through parallel computation (the group owns and maintains a HPC cluster). The group already has a widely recognized expertise and prestige in these fields, and we plan to continue working on them in the following years.

  • 2.

    Dynamical Systems at UPC

    The mail goal of the project is the research in Dynamical Systems from two complementary points of view. A theoretical approach, focusing in challenging problems like: a) Arnold diffusion; b) Splitting of separatrices; c) Integrability; d) Bifurcations, normal forms and computation of invariant objects; e) Quasi-periodic dynamics; f) Numerical computation and computer assisted proofs; g) Infinite dynamical Systems; h) Mathematical physics. As well as a focus in practical applications like: a) Astrodynamics; b) Celestial Mechanics; c) Non-smooth Systems; d) Mathematical and computational neuroscience; e) Other applications to Physics and chemistry.

  • 3.

    Brazilian European Partnership in Dynamical Systems (BREUDS)

    This grant is devoted to the interchange of researchers between groups in Dynamical Systems from European universities and Brazilian universities. The grant focuses in different areas of Dynamical Systems like Hamiltonian Dynamics, non-smooth dynamics, etc

Bioinformatics services offered

  • Modeling, simulation and analysis of neural activity

    The group has been developing research on mathematical and computational neuroscience for the last 15 years, performing modeling, simulation and analysis of neural activity. In particular, studying oscillations and synchronization, activity patterns in cognitive processes and neuronal communication. We have also experience in building up and study mathematical and statistical models of epidemiology and bifurcation analysis in population dynamics. The group offers expertise in explaining biological mechanims through simplified models by means of the theory of dynamical systems, in applying advanced numerical methods for ordinary differential equations, parameter estimation techniques and bifurcation analysis. We are increasingly involved as well in applying stochastic processes to the abovementioned biological problems.The computations of the projects in which the group is involved can be launched in the High-Performance Computing cluster called “Eixam”. The members of the group working in this topics have ong experience collaborating with experimental groups, both in electrophysiology, psychology, population biologists and epidemiologists. As a consequence, they master the common language of biology and are optimal interlocutors for multidisciplinary projects to talk to experimentalists or non-academic partners.