AI 中文总结
本研究从确定性与熵视角，通过5000×5000分辨率扫描Ω-F参数平面，揭示受迫耗散杜芬系统中阿诺德舌的宏观锁相区域与微观流形交点的关系，明确同宿交点区域是混沌显现区域的必要条件。
AI 中文摘要
耗散混沌常表现出向周期窗口或消失态的突变，但这些突变发生在远低于梅尔尼科夫阈值等宏观理论边界的位置。本研究从确定性和熵的视角重新评估参数空间中受迫输入同步所呈现的“阿诺德舌”的不变流形的横向交点（微观）。我们应用一种算法，以二进制值（1.0或0.0）的形式数字确定流形交点，不使用数值插值。在阻尼系数固定为k=0.2的情况下，以5000×5000（2500万个点）的分辨率扫描Ω-F参数平面，得以全局捕捉阿诺德舌所呈现的宏观锁相区域与微观流形交点（混沌区域）之间的关系。此外，从计算精度经检验的一维截面中，我们确认了一种动力学情形：同宿交点区域（拓扑熵h_T>0）是混沌显现区域（柯尔莫哥洛夫-西奈熵h_KS>0）的必要条件，同时也确认了初级鞍点解的交点不作为必要条件的区域的存在。
英文摘要
Dissipative chaos often exhibits abrupt transitions to periodic windows or vanishing states, but these transitions occur far below macroscopic theoretical boundaries such as the Melnikov threshold. In this study, we re-evaluate the transversal intersections (microscopic) of invariant manifolds from a deterministic and entropic perspective for the ``Arnold tongues'' shown by synchronization to forced inputs in the parameter space. We applied an algorithm that digitally determines manifold intersections as binary values ($1.0$ or $0.0$) without numerical interpolation. As a result of scanning the $Ω- F$ parameter plane at a resolution of $5000 \times 5000$ ($25$ million points) with the damping coefficient fixed at $k = 0.2$, it became possible to globally capture the relationship between the macroscopic phase-locked regions shown by the Arnold tongues and the microscopic manifold intersections (chaotic regions). Furthermore, from a one-dimensional cross-section whose computational accuracy was verified, we confirmed a dynamical case where the region with homoclinic intersections (topological entropy $h_T > 0$) is a necessary condition for the region where chaos manifests (Kolmogorov-Sinai entropy $h_{KS} > 0$), and simultaneously confirmed the existence of a region where the intersection of the primary saddle solution does not serve as a necessary condition.
Comments6 pages and 3 figures
