Biomedical subjects

João Corte-Real

Publications and source records attributed to João Corte-Real.

3 recordsLinked to original sources

PubMed2004

Pattern formation in diffusive-advective coupled map lattices.

We investigate pattern formation and evolution in coupled map lattices when advection is incorporated, in addition to the usual diffusive term. All patterns may be suitably grouped into five classes: three periodic, supporting static patterns and traveling waves, and two nonperiodic. Relative frequencies are determined as a function of all model parameters: diffusion, advection, local nonlinearity, and lattice size. Advection plays an important role in coupled map lattices, being capable of considerably altering pattern evolution. For instance, advection may induce synchronization, making chaotic patterns evolve periodically. As a byproduct we describe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of traveling waves.

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PubMed2004

Inducing coherence in networks of bistable maps by varying the interaction range.

Ordinarily, two different topologies have been used to model spatiotemporal chaos and to study complexity in networks of maps: one where sites interact only with nearest neighbors (e.g., the standard diffusive coupling) and one where sites interact with all sites in the network (global coupling). Here we investigate intermediate regimes considering the interaction range as a free tunable parameter. The synchronization behavior normally seen in globally coupled maps is found to set in for interaction ranges considerably smaller than the system size. In addition, we analytically derive stability conditions for the onset of coherent states (full synchronization) from which the minimum interaction range needed to induce coherence in homogeneously coupled maps can be determined. Such conditions are also obtained for inhomogeneous situations when the coupling strength decreases linearly with the distance. The characteristic range for the onset of coherence is studied in detail as a function of model parameters.

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PubMed2002

Modeling velocity in gradient flows with coupled-map lattices with advection.

We introduce a simple model to investigate large scale behavior of gradient flows based on a lattice of coupled maps which, in addition to the usual diffusive term, incorporates advection, as an asymmetry in the coupling between nearest neighbors. This diffusive-advective model predicts traveling patterns to have velocities obeying the same scaling as wind velocities in the atmosphere, regarding the advective parameter as a sort of geostrophic wind. In addition, the velocity and wavelength of traveling wave solutions are studied. In general, due to the presence of advection, two regimes are identified: for strong diffusion the velocity varies linearly with advection, while for weak diffusion a power law is found with a characteristic exponent proportional to the diffusion.

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