基于动态耦合的异质有向超图同步
Synchronization of directed hypergraphs with heterogeneities via dynamic coupling
- University of Naples Federico II（那不勒斯费德里科二世大学）
- Scuola Superiore Meridionale（南方高等学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对含参数失配的非线性智能体有向超图，提出基于动态耦合的主稳定性函数框架，通过比例-积分耦合实现完全同步，并在Lorenz振子及非线性意见动力学中验证了方法有效性。
AI中文摘要：
许多真实世界的网络包含三个及以上智能体之间的相互作用，且无法简化为两两耦合，这使得超图成为一种自然的建模框架。本研究探讨了在动态扩散耦合下，存在参数失配的非线性智能体有向超图中的完全同步问题。尽管比例-积分耦合方案已知可在异质线性网络中实现共识，但它们在非线性系统中实现完全同步的能力更为有限，通常仅能产生有界同步。我们证明，只有当参数失配的效应在横向动力学中结构上等价于恒定扰动时，才能实现完全同步。在此条件下，我们推导了同步流形的不变性和局部稳定性条件，并开发了适用于动态耦合有向超图的主稳定性函数框架。该方法考虑了不同的比例和积分超图层，并提供了预测同步区域的谱准则。对Lorenz振子有向超图的数值模拟验证了理论预测，并展示了积分作用如何补偿比例层引起的去稳定效应。我们进一步证明了该框架在非线性意见动力学的牵制控制问题中的适用性，其中动态扩散耦合在存在异质性的情况下实现了完全的主从共识。
英文摘要：
Many real-world networks involve interactions among three or more agents that cannot be reduced to pairwise coupling, making hypergraphs a natural modeling framework. In this work, we study complete synchronization in directed hypergraphs of nonlinear agents with parameter mismatches under dynamic diffusive coupling. Although proportional-integral coupling schemes are known to achieve consensus in heterogeneous linear networks, their ability to enforce complete synchronization in nonlinear systems is more limited, generally yielding only bounded synchronization. We show that complete synchronization can be attained only when the effect of parameter mismatches is structurally equivalent, in the transverse dynamics, to a constant disturbance. Under this condition, we derive invariance and local stability conditions for the synchronization manifold and develop a Master Stability Function framework for directed hypergraphs with dynamic coupling. The proposed approach accounts for distinct proportional and integral hypergraph layers and provides spectral criteria for predicting synchronization regions. Numerical simulations on directed hypergraphs of Lorenz oscillators validate the theoretical predictions and show how the integral action can compensate destabilizing effects induced by the proportional layer. We further demonstrate the applicability of the framework to a pinning-control problem in nonlinear opinion dynamics, where dynamic diffusive coupling achieves complete leader-follower consensus in the presence of heterogeneity.
