Higher Order Interactions in Hub Neural Networks: Spatiotemporal Dynamics Reshaping and Control
本文提出一个包含高阶相互作用的受控扩散枢纽神经网络模型，并引入跨节点关联延迟反馈控制方法，分析了局部稳定性、图灵不稳定性和Hopf分岔条件，发现高阶相互作用对动力学影响较小，而控制方法能有效优化时空动力学。
The study of dynamics in complex systems has increasingly incorporated higher order interactions, which capture the collective influence among three or more units, extending beyond traditional pairwise connections. Although such interactions are observed in biological neural networks, their precise role in shaping network dynamics and the feasibility of controlling these dynamics remain unclear. This article proposes a controlled diffusion hub neural network model that explicitly includes higher order interactions. To regulate the resulting spatiotemporal dynamics, a cross-node associated delayed feedback control (CNADFC) method is further introduced. Our analysis establishes conditions for local stability, Turing instability, and Hopf bifurcation. We show that while Turing instability cannot arise, spatially periodic patterns emerge under specific parametric conditions. Numerical simulations confirm these theoretical findings and highlight the pronounced effects of self-feedback, control, and first-order interaction on stability and dynamic behaviors; in contrast, higher order interactions exert a comparatively modest influence. Furthermore, simulations illustrate how the CNADFC method can effectively optimize spatiotemporal dynamics. This work advances the understanding of diffusion neural network behavior under complex higher order interaction and provides a reference for the effective control of such networks.