A simple scalar coupled map lattice (sCML) model for excitable media is derived in this paper. The new model, which has a simple structure, is shown to be closely related to the observed phenomena in excitable media. Properties of the sCML model are also investigated. Illustrative examples show that this kind of model is capable of reproducing the behavior of excitable media and of generating complex spatiotemporal patterns.
The identification problem for excitable media is investigated in this paper. A new scalar coupledmap lattice (SCML) model is introduced and the orthogonal least squares algorithm is employedto determinate the structure of the SCML model and to estimate the associated parameters. Asimulated pattern and a pattern observed directly from a real Belousov-Zhabotinsky reactionare identified. The identified SCML models are shown to possess almost the same local dynamicsas the original systems and are able to provide good long term predictions.
In this brief, by combining an efficient wavelet representationwith a coupled map lattice model, a new family of adaptive wavelet neuralnetworks, called lattice dynamical wavelet neural networks (LDWNNs),is introduced for spatio-temporal system identification. A new orthogonalprojection pursuit (OPP) method, coupled with a particle swarm optimization(PSO) algorithm, is proposed for augmenting the proposed network.A novel two-stage hybrid training scheme is developed for constructing aparsimonious network model. In the first stage, by applying the OPP algorithm,significant wavelet neurons are adaptively and successively recruitedinto the network, where adjustable parameters of the associated waveletneurons are optimized using a particle swarm optimizer. The resultant networkmodel, obtained in the first stage, however, may be redundant. In thesecond stage, an orthogonal least squares algorithm is then applied to refineand improve the initially trained network by removing redundant waveletneurons from the network. An example for a real spatio-temporal systemidentification problem is presented to demonstrate the performance of theproposed new modeling framework.
