发布时间：2025-09-09
Stability of uniformly incoherent state in the D-dimensional generalized Kuramoto model
主讲人：邹为
摘要：In this work, we are devoted to theoretically analyzing the stability of the completely incoherent state in the D-dimensional generalized Kuramoto model within the same one framework, where a completely incoherent state refers to that all agents are uniformly distributed on surface S of the unit sphere in D-dimensional space. By linearizing the continuity equation of the model in its thermodynamic limit, we obtain the characteristic equation that governs the linear stability of the uniformly incoherent state for arbitrary dimension with D >= 2. Moreover, we show that all the stability information regarding the complete incoherence can be successfully retrieved from the reduced system via high- dimensional Ott–Antonsen ansatz for the D-dimensional generalized Kuramoto model. For a Gaussian ensemble of natural rotations, we demonstrate that the characteristic equation can be explicitly simplified for both even and odd D. In particular, via the simplified characteristic equation, we verify theoretically that the critical coupling strength for the instability of the uniformly incoherent state is always retained at zero for all odd D>=3. Our study provides a detailed recipe for the stability analysis of complete incoherence in the D-dimensional generalized Kuramoto model, which is potential for identifying the onset of phase transition to synchrony in systems of interacting high-dimensional heterogeneous agents.
主讲人简介：邹为，华南师范大学数学科学学院教授、博士生导师，先后获聘德国洪堡学者，香港香江学者，广东青年珠江学者。长期致力于复杂系统、非线性科学理论研究，在复杂耦合非线性系统的集体动力学行为研究问题上取得系列成果。目前已在非线性动力学主流学术期刊发表SCI论文50余篇，其中以第一作者发表2篇Physical Review Letters、1篇Nature Communications及1篇Physics Reports，主持两项自然科学基金面上项目，现任中国物理学会Chin. Phys. Lett.、Chin. Phys. B、物理学报和物理四刊联合青年编委。
邀请人：李东方
时间：2025年9月13日18:00-20:00
地点： 腾讯会议室： 977840330