The Computational Dynamics Group (CODY) applies and develops theoretical and computational tools and methodologies in an interdisciplinary environment for understanding the behavior of nonlinear systems in different settings:

Topics

Biomathematics

Numerical and analytical study of mathematical models in Biomathematics.

  • Mathematical neuroscience. Mathematical neuron models, bifurcation analysis, design of new computational tools in neuroscience, fast-slow systems, bursting-spiking transition, coupled neuron systems (CPGs), neuron networks.
  • Non-linear cardiac dynamics. Mathematical myocyte models, bifurcation analysis, design of new computational tools in cardiac dynamics, cardiac arrhythmia.

Dynamical Systems

Development of new numerical methods for dynamical systems problems. Theoretical study of models.

  • Dissipative systems. Low dimensional systems, crossroad formation in parameter space, homoclinic codimension-2 bifurcations, hyperchaos, periodically forced systems.
  • Computer Assisted Proofs. Rigorous proof of the existence of invariants.
  • Computational tools. Perturbation theory, bifurcation analysis, parameter sweeping techniques, Lyapunov exponents, chaos indicators.

Numerical Analysis

Design and theoretical study of new methods in Numerical Analysis, focusing in applications to Dynamical Systems

  • ODE and DAE systems. New numerical methods for ODEs, Taylor Series method.
  • Numerical linear algebra. Stability theory, evaluation of special functions, optimization algorithms, orthogonal polynomials and applications
  • High-precision numerical analysis. High-precision numerical linear algebra, high-precision solution of ODEs, rigorous computing.
Full list of publications

Recent publications

  1. T. Sun, R. Barrio, L. Cheng and H. Jiang. Precompact convergence of the nonconvex Primal–Dual Hybrid Gradient algorithm, Journal of Computational and Applied Mathematics 330 (2018) 15–27.
  2. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. Supressors of selection, Plos One 12 7 (2017) e0180549. doi 10.1371/journal.pone.018054910.1371
  3. F. Alcalde Cuesta, P. González Sequeiros and Á. Lozano Rojo. A method for validating Rent’s rule for technological and biological networks, Scientific Reports 7 (2017) 5378. doi 10.1038/s41598-017-05670-w
  4. F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo and R. Vigara Benito. An accurate database of the fixation probabilities of all undirected graphs of order 10 or less, In Bioinformatics and Biomedical Engineering IWBBIO2017, Lecture Notes in Computer Science 10209, 2017. doi 10.1007/978-3-319-56154-7_20.
  5. D. Wilczak and R. Barrio. Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori, SIAM Journal on Applied Dynamical Systems 16 3 (2017) 1618–1649.
  6. R. Barrio, S. Ibáñez and L. Pérez. Hindmarsh–Rose model: Close and far to the singular limit, Physics Letters A 381 6 (2017) 597–603.
  7. P. Du, R. Barrio, H. Jiang and L. Cheng. Accurate Quotient-Difference algorithm: error analysis, improvements and applications, Applied Mathematics and Computation 309 (2017) 245–271.
  8. F. Alcalde Cuesta, Á. Lozano Rojo and A. C. Vázquez. Insertion-tolerance and repetitiveness of random graphs, Stochastics & Dynamics 17 3 (2017) 1750023. doi 10.1142/S021949371750023X
  9. V. Salas-Fumás, C. Sáenz and Á. Lozano Rojo. Organisational Structure and Performance of Consensus Decisions through Mutual Influences: A Computer Simulation Approach, Decision Support Systems 86 (2016) 61–72. doi 10.1016/j.dss.2016.03.008
  10. M. Á. Marco-Buzunariz and M. Rodríguez. SIROCCO: A Library for Certified Polynomial Root Continuation, In International Congress on Mathematical Software, 2016.