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:
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.
Control strategies of 3-cell Central Pattern Generator via global
, and . Scientific reports 6 (2016) 23622.
Mechanism of quasi-periodic lag jitter in bursting rhythms by a
, , and . Europhysics Letters 112 3 (2015) 38002.
Macro-and micro-chaotic structures in the Hindmarsh-Rose model of
, , and . Chaos: An Interdisciplinary Journal of Nonlinear Science 24 2 (2014) 023128.
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.
Coexistence and dynamical connections between hyperchaos and chaos
in the 4D Rössler system: A computer-assisted proof.
, and . SIAM Journal on Applied Dynamical Systems 15 1 (2016) 356-390.
Topological changes in periodicity hubs of dissipative systems.
, and . Physical Review Letters 108 21 (2012) 214102.
Qualitative analysis of the Rössler equations: Bifurcations of
limit cycles and chaotic attractors.
, and . Physica D: Nonlinear Phenomena 238 13 (2009) 1087-1100.
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.
A general condition number for polynomials
, and . SIAM Journal on Numerical Analysis 51 2 (2013) 1280-1294.
Algorithm 924: Tides, a Taylor series integrator for differential
, , and . ACM Transactions on Mathematical Software 39 1 (2012) 5.
Sensitivity analysis of ODEs/DAEs using the Taylor series method.
. SIAM Journal on Scientific Computing 27 6 (2006) 1929-1947.
- Precompact convergence of the nonconvex Primal–Dual Hybrid Gradient algorithm, Journal of Computational and Applied Mathematics 330 (2018) 15–27. , , and .
- Supressors of selection, Plos One 12 7 (2017) e0180549. doi 10.1371/journal.pone.018054910.1371 , and .
- A method for validating Rent’s rule for technological and biological networks, Scientific Reports 7 (2017) 5378. doi 10.1038/s41598-017-05670-w , and .
- 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. , , and .
- 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. and .
- Hindmarsh–Rose model: Close and far to the singular limit, Physics Letters A 381 6 (2017) 597–603. , and .
- Accurate Quotient-Difference algorithm: error analysis, improvements and applications, Applied Mathematics and Computation 309 (2017) 245–271. , , and .
- Insertion-tolerance and repetitiveness of random graphs, Stochastics & Dynamics 17 3 (2017) 1750023. doi 10.1142/S021949371750023X , and .
- 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 , and .
- SIROCCO: A Library for Certified Polynomial Root Continuation, In International Congress on Mathematical Software, 2016. and .