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

我们利用耦合映射格（CML）研究了高维混沌的特征，包括时空混沌。我们特别澄清了以下特点。研究了开流CML的模式动力学。发现了具有时间周期性的空间混沌，并用共移李雅普诺夫指数分析了混沌的稳定性。发现了混沌缺陷周期晶格的组织，用动力系统理论解释了其机理，而在较强的非线性中发现了混沌缺陷的间歇跃迁。研究了开放流模型中吸引子的选择和周期输入的放大传播。该研究通过微小的输入导致了模式的可控性。讨论了在信息处理中的可能应用。在具有吸引力和排斥力的哈密顿系统中分别发现了两种有序态：聚类态和分散态。各种有序态依赖于初始条件共存，在相空间中形成洋葱状结构。这一发现给出了多粒子系统中秩序形成的新机制。分析了贝纳德对流的CML，它再现了所有已知的实验现象，并得出了一些关于湍流行为和混沌流动的新预测。在全局耦合地图系统中发现了级联信息流，并研究了各种耦合地图系统中元素间关系的混沌流变性和动态性。讨论了它们与生物信息处理的相关性。

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.