Variety of dynamics in high-dimensional chaotic dynamical systems

在实际和虚拟（计算机）实验中都可以观察到高维动力系统动力学的变化。它可以被认为是一种瞬态运动。发现了一个典型的现象。十年前，这个项目的首席研究员在非平衡神经网络中发现了混沌流动。最近，这个项目的研究人员发现了反应扩散系统中一个复杂的瞬态运动，它是由许多对鞍和节点同时湮灭而产生的。这个项目的目的是研究与鞍节点的产生和消灭有关的混沌流动机制。我们在计算机实验中观察到，我们称之为吸引子毁灭的准吸引子可以用米尔诺吸引子来描述。引入分岔参数并改变分岔参数，研究了耦合Milnor吸引子系统对耦合鞍-节点系统的连续性。因此，我们发现了这两个系统的连续性。此外，我们发现即使在耦合鞍节点接近的临界点附近，盆地边界也存在千孔。因此，我们可以合理地说，千孔百孔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.