高阶相互作用诱导异常过渡到同步
Iván León1,2, Riccardo Muolo3, Shigefumi Hata4
1Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan.
Chaos (Woodbury, N.Y.)
|January 9, 2024
概括
结合相振荡器中的高阶相互作用会导致不寻常的同步行为,包括多个稳定状态和新的过渡路径. 这些发现超出了标准库拉莫托模型的范围,即使有振荡器频率变化.
科学领域:
- 非线性动力学是一种非线性动力学.
- 复杂的系统复杂的系统.
- 统计物理学的统计物理.
背景情况:
- 偶联的非线性振荡器在各种科学领域都是基本的.
- 库拉莫托模型是研究振荡器同步的一个标准.
- 高阶相互作用和相位延迟往往被简化或忽略.
研究的目的:
- 分析双体和三体相互作用的合相振荡器的最小模型,包括顺序对称和相滞后.
- 研究高阶相互作用对同步现象的影响.
- 探索异常过渡到同步和相关的动态模式.
主要方法:
- 弱合非线性振荡器的相位减小.
- 简化模型的理论分析与更高层次的相互作用.
- 构建动态模式的相位图.
- 通过直接的数值模拟进行验证.
主要成果:
- 高阶相互作用诱导异常过渡到同步.
- 观察到完全同步,不连贯和两个集群状态的多稳定性.
- 过渡到同步发生通过缓慢切换和集群.
- 类似的过渡场景甚至在微小的振荡器频率异质的情况下也存在.
结论:
- 与传统的库拉莫托模型相比,高阶相互作用的包含显著改变了同步动态.
- 异常同步现象,包括多稳定性和新的过渡路径,是高阶合系统的特征.
- 该模型为理解各种系统中复杂的同步行为提供了一个框架,即使在异质性下也是如此.
相关概念视频
¹H NMR: Interpreting Distorted and Overlapping Signals
1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.0K
Cooperative Allosteric Transitions
7.9K
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
7.9K
¹H NMR: Long-Range Coupling
1.8K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
1.8K
Phase Transitions
19.1K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
19.1K
¹H NMR Signal Multiplicity: Splitting Patterns
5.2K
When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
5.2K
NMR Spectroscopy: Spin–Spin Coupling
1.4K
The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
1.4K


