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.
Numerical detection of patterns in CPGs: Gait patterns in insect movement.
, , and . Communications in Nonlinear Science and Numerical Simulation 82 (2020) 105047.
Bifurcations and slow-fast analysis in a cardiac cell model for investigation of early afterdepolarizations.
, , and . Mathematics 8 6 (2020) 880.
Control strategies of 3-cell Central Pattern Generator via global
, and . Scientific reports 6 (2016) 23622.
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.
Spike-adding structure in fold/hom bursters.
, , and . Communications in Nonlinear Science and Numerical Simulation 83 (2020) 105100.
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.
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.
ORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives.
, , and . Computer Physics Communications 231 2 (2018) 146–162.
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.
- Excitable dynamics in neural and cardiac systems, Communications in Nonlinear Science and Numerical Simulation 86 (2020) 105275. , , , , and .
- Homoclinic organization in the Hindmarsh–Rose model: A three parameter study, Chaos: An Interdisciplinary Journal of Nonlinear Science 30 5 (2020) 22106. , and .
- Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880. , , and .
- 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. and .
- Experimentally accessible orbits near a Bykov cycle, International Journal of Bifurcation and Chaos 30 10 (2020) 2030030. , , and .
- Range searching in multidimensional databases using navigation metadata, Applied Mathematics and Computation 386 (2020) 125510. doi 10.1016/j.amc.2020.125510 and .
- 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 , , and .
- Spike-adding structure in fold/hom bursters, Communications in Nonlinear Science and Numerical Simulation 83 (2020) 105100. doi 10.1016/j.cnsns.2019.105100 , , and .
- Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880. doi 10.3390/math8060880 , , and .
- Convergence rates of accelerated proximal gradient algorithms under independent noise, Numerical Algorithms 81 2 (2019) 631–654. , , and .