How to Predict Bifurcations Induced by Fractional Order in Delayed Large-Scale Neural Networks

作者：Yunxiang Lu, Min Xiao, Leszek Rutkowski, Zhengxin Wang, Xiaoqun Wu, Zhen Wang, Chengdai Huang, Jinde Cao, Wei Xing Zheng · 发表于：IEEE Transactions on Cybernetics · 年份：2025 · DOI：10.1109/tcyb.2025.3585240 · 被引用次数：5 · 研究领域：Neural Networks and Applications

The principal innovative contribution of this study resides in the introduction of a category of fractional delayed large-scale neural networks characterized by intricate topological structures. Additionally, this article provides a comprehensive exploration of novel outcomes linked to fractional order-induced bifurcations in large-scale networks. In the initial step, the correlation of the artificial neural network and the graphical neural network is established through the Mason's diagram method. Subsequently, the system's characteristic equations are derived by employing the Coates' flow graph decomposition method. Moving on, through the concept of the global element, an exhaustive investigation delves into the distribution of eigenroots. The sum of synaptic transmission delays among neurons is considered as a bifurcation parameter, with an analysis focused on the stability of the trivial equilibrium and the existence of the Hopf bifurcation. Following this, the optimal fractional order-dependent stability interval is determined using the implicit function array curve method, presenting a novel approach for critical value determination. Finally, the drawn conclusions are substantiated through multiple sets of computer simulations. It is indicated that an increase in delay precipitates the onset of Hopf bifurcation. Moreover, a reduction in the fractional order significantly improves the steady-state performance of the system. However, once the fractional order value descen...