Study of Response, Propagation, and Reconstruction of High-dimensional Chaos with Coupled Maps

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We have studied features of high-dimensional chaos, including spatiotemporal chaos by means of coupled map lattices (CML). In particular we have clarified the following features.1.The pattern dynamics of the open-flow CML is studied. Spatial chaos with temporal periodicity is found, whose stability is analyzed by the co-moving Lyapunov exponents. Organization of periodic lattice of chaotic defects is found, whose mechanism is explained by the dynamical systems theory, while intermittent transition of such defects is found in stronger nonlinearity.2.Selection of attractors and amplified propagation of periodic inputs are studied in the open flow model. The study leads to the controalbility of patterns by tiny inputs. Possible applications to information processings are discussed.3.Two types of ordered states, clustered and dispersed states are found in Hamiltonian system with attractive and repulsive forces respectively. A variety of ordered states coexist depednding on initial conditions, which form onion structures in the phase space. This discovery gives a novel mechanism of order formation in many-particle systems.4.CML for Benard convection is analyzed, which reproduces all known phenomena in experiments and leads to several novel predictions on turbulent behaviors and chaotic itinerancy.5.The cascade information flow is found in globally coupled maps, while the chaotic itinerancy and dynamics of relationships between elements are studied in a variety of coupled map systems. Their relevenace to biological information prcoessings are discussed.