The identification of complex spatiotemporal patterns using Coupled map lattice model

Many complex and interesting spatiotemporal patterns have been observed in a wide range of scienti¯c areas. In this paper, two kinds of spatiotemporal patterns including spot replication and Turing systems are investigated and new identi¯cation methods are proposed to obtain Coupled Map Lattice (CML) models for this class of systems. Initially, a new correlation analysis method is introduced to determine an appropriate temporal and spatial data sampling step procedure for the identification of spatiotemporal systems. A new combined Orthogonal Forward Regression and Bayesian Learning algorithm with Laplace priors is introduced to identify sparse and robust CML models for complex spatiotemporal patterns. The final identified CML models are validated using correlation based model validation tests for spatiotemporal systems. Numerical re-sults illustrate the identification procedure and demonstrate the validity of the identified models.