Variety of dynamics in high-dimensional chaotic dynamical systems

高维动力学系统的动力学变化可以在实际和虚拟（计算机）实验中观察到。它可以被识别为瞬态运动。一个典型的现象已经被发现，十年前该项目的首席研究员在非平衡神经网络中发现了混沌巡游。最近，本课题的研究人员在反应扩散系统中发现了一种复杂的瞬态运动，它是由多对鞍点和节点同时湮灭引起的。本计画的目的是探讨与鞍结产生与湮灭有关的混沌巡游机制。我们在计算机实验中观察到，我们称之为吸引子破产的拟吸引子可以用Milnor吸引子来描述。通过引入分歧参数并改变分歧参数，研究了耦合Milnor吸引子系统到耦合鞍结系统的连续性。因此，我们发现了这两个系统的连续性。此外，我们发现，甚至在附近的临界点接近的情况下，鞍结耦合的千疮百孔的盆地边界。因此，我们可以说，这个充满漏洞的盆地边界变成了连接米尔诺吸引子的混沌轨道。

The Variety of dynamics in high-dimensional dynamical systems can be observed in both actual and virtual (computer) experiments. It may be identified as a transient motion. A typical phenomenon has been found. The head investigator of this project found chaotic itinerancy in nonequilibrium neural networks, ten years ago. Recently the investigators of this project found a complex transient motion in reaction-diffusion systems, which is derived from a simultaneous annihilation of many pairs of saddle and node. The purpose of this project is to investigate a mechanism of chaotic itinerancy in relation with a creation and annihilation of saddle-node. We observed in computer experiments that a quasiattractor which we called an attractor ruin can be described by a Milnor attractor. Introducing a bifurcation parameter and changing it, we investigated a continuity of a coupled Milnor attractor system to a coupled saddle-node system. Consequently, we found the continuity of these two systems. Furthermore, we found riddled basin boundaries even in the neighborhood of the critical point approached from the case of coupled saddle-node. Therefore, it is plausible to state that the riddled basin boundaries become chaotic orbits that link Milnor attractors.