Biomedical subjects

E Hernández-García

Publications and source records attributed to E Hernández-García.

14 recordsLinked to original sources

PubMed2001

Quasiperiodic patterns in boundary-modulated excitable waves.

We investigate the impact of domain shape on wave propagation in excitable media. Channeled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration that repeats periodically in time. The phenomenon is numerically studied in a model for a photosensitive Belousov-Zabotinsky reaction. Spatial return maps for the height and position of the successive fronts are analytically obtained, and reveal the similarity between this spatial quasiperiodicity and the temporal quasiperiodicity appearing in forced oscillators.

Journal Article↗

PubMed2001

Complex Ginzburg-Landau equation in the presence of walls and corners.

We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of two-dimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern. Corners between walls provide additional synchronization mechanisms and associated selection criteria. The numerical results fit well with the theoretical predictions in the parameter range studied.

Journal Article↗

PubMed2000

Forecasting confined spatiotemporal chaos with genetic algorithms.

A technique to forecast spatiotemporal time series is presented. It uses a proper orthogonal or Karhunen-Loève decomposition to encode large spatiotemporal data sets in a few time series, and genetic algorithms to efficiently extract dynamical rules from the data. The method works very well for confined systems displaying spatiotemporal chaos, as exemplified here by forecasting the evolution of the one-dimensional complex Ginzburg-Landau equation in a finite domain.

Algorithms↗

PubMed1999

Frozen spatial chaos induced by boundaries.

We show that rather simple but nontrivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.

Journal Article↗

PubMed1996