Research Institute for Electronic Science, Hokkaido University, Kita-ku, Sapporo, Japan.
Chaos. 2009 Sep;19(3):033132. doi: 10.1063/1.3212934.
In this paper, we study a dynamic structure of discretized vector fields obtained from the Brusselator, which is described by two-dimensional ordinary differential equations (ODEs). We found that a bifurcation structure of the logistic map is embedded in the discretized vector field. The embedded bifurcation structure was unraveled by the dynamical orbits that eventually converge to a fixed point. We provide a detailed mathematical analysis to explain this phenomenon and relate it to the solution of the original ODEs.
在本文中，我们研究了由二维常微分方程（ODE）描述的布鲁塞尔ator 离散化向量场的动态结构。我们发现，逻辑映射的分岔结构嵌入在离散化向量场中。通过最终收敛到一个平衡点的动力学轨道，揭示了嵌入的分岔结构。我们提供了详细的数学分析来解释这一现象，并将其与原始 ODE 的解联系起来。
