Study on the emergent mechanism of macroscopic dynamical structure in large dimensional dynamical systems

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We studied on structures in phase space of large dimensional dynamical systems, that attract and hold trajectories for a considerable duration while they are not completely stable. Such structures are assumed to play an essential role in the emergence of slow dynamics with long tail in temporal correlation. We adopted globally coupled chaotic map systems as the main working model, and as a result of the research, we uncovered a type of psudo attractors in large dimensional chaotic systems, that can appear quite commonly and robustly. The psudo attractors of known types (especially in the dynamical systems with small number of degrees of freedom are basically remnant of attractor that collide with its basin boundary, and therefore observed only in quite limited area in parameter space, on the other hand, the newly uncovered ones can ovserved in broad area in the parameter space, since they are saddle set that are associated to the attractors in the dynamical system of continuous distribution, which corresponds to a limit of infinitely many degrees of freedom. The result obtained here would supply a basic idea to understand the behavior of the systems which is not completely disordered in spite of its essentially irreducible large number of degrees of freedom, a class of phenomena that are quite ubiquitous in so called complex systems. In addition to the above mentioned result, we found some novel phenomena in dynamical systems with small number of degrees of freedom, that are also related to slow dynamics like intermittency or itinerancy, and have a kind of robustness, and possibly be observed in the systems with a certain class of symmetry. The results show that there still much to explore in this area, the dynamics of complex systems, while they provide some clue to analyze quasi-stable states in such systems.