Research

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. R. Barrio, S Coombes, M Desroches, F Fenton, S Luther and E Pueyo. Excitable dynamics in neural and cardiac systems, Communications in Nonlinear Science and Numerical Simulation 86 (2020) 105275.
  2. R. Barrio, S. Ibáñez and L. Pérez. Homoclinic organization in the Hindmarsh–Rose model: A three parameter study, Chaos: An Interdisciplinary Journal of Nonlinear Science 30 5 (2020) 22106.
  3. R. Barrio, M. Á. Martínez, L. Pérez and E Pueyo. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880.
  4. R. Barrio and D Wilczak. Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon–Heiles system, Nonlinear Dynamics 102 1 (2020) 403–416.
  5. MP de Carvalho, R. Barrio, A. Rodrigues and ML Castro. Experimentally accessible orbits near a Bykov cycle, International Journal of Bifurcation and Chaos 30 10 (2020) 2030030.
  6. D. Arnas and M. Rodríguez. Range searching in multidimensional databases using navigation metadata, Applied Mathematics and Computation 386 (2020) 125510. doi 10.1016/j.amc.2020.125510
  7. R. Barrio, Á. Lozano, M. Rodríguez and S. Serrano. Numerical detection of patterns in CPGs: Gait patterns in insect movement, Communications in Nonlinear Science and Numerical Simulation 82 (2020) 105047. doi 10.1016/j.cnsns.2019.105047
  8. R. Barrio, S. Ibáñez, L. Pérez and S. Serrano. Spike-adding structure in fold/hom bursters, Communications in Nonlinear Science and Numerical Simulation 83 (2020) 105100. doi 10.1016/j.cnsns.2019.105100
  9. R. Barrio, M. Á. Martínez, L. Pérez and E Pueyo. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880. doi 10.3390/math8060880
  10. T Sun, R. Barrio, H Jiang and L Cheng. Convergence rates of accelerated proximal gradient algorithms under independent noise, Numerical Algorithms 81 2 (2019) 631–654.