Stability Switching and Oscillation Regulation Strategies for Large-Scale Fractional-Order Neural Networks With Double Hubs and Multiple Delays
提出一种仅作用于单个枢纽节点的低维状态反馈控制策略，抑制双枢纽耦合分数阶神经网络中的Hopf分岔，降低实现复杂度，并揭示网络规模、分数阶阶次和枢纽连接对振荡的影响。
Abnormal neuronal oscillations underlie various brain disorders; however, effective regulation remains challenging due to the inherent complexity of neural network (NN) dynamics. This article proposes a hub-targeted state-feedback control strategy acting exclusively on a single hub node to suppress Hopf bifurcation in $(n{\,}+{\,}m)$ -dimensional dual-hub coupled NNs governed by fractional-order differential equations with multiple time delays. Unlike conventional full-dimensional controllers requiring state measurements from all nodes, the proposed low-dimensional controller significantly reduces implementation complexity and sensing overhead. The characteristic equation of the high-order multidelay system is derived via the Coates flow graph method, and rigorous delay-dependent bifurcation criteria are established based on fractional stability theory and the Hopf bifurcation theorem. Numerical simulations validate the theoretical predictions, demonstrating that an appropriately tuned control gain effectively postpones oscillation onset and enhances robustness against parameter perturbations. Furthermore, the bifurcation threshold is shown to be highly sensitive to fractional-order variations, while larger network scales promote high-frequency oscillations. Notably, interhub connectivity is identified as a critical trigger for periodic oscillations, and hub-node failure is found to enlarge the stability region by degrading the dual-hub topology to a single-hub configuration.