From Pairwise to Higher-Order Interactions: Stability Switching of Fractional-Order BAM Neural Networks
研究了分数阶双向联想记忆神经网络在高阶交互下的稳定性切换，发现适当引入弱高阶交互可提高分岔阈值并抑制振荡，为复杂网络系统设计提供理论指导。
When modeled as complex networked dynamical systems, conventional neural networks, which predominantly rely on pairwise (first-order) interactions, often prove inadequate in capturing complex group dynamics. As these systems are extended to incorporate higher-order interactions, their dynamical behaviors become increasingly intricate. Consequently, within the scope of systems engineering, analyzing the stability boundaries is crucial for ensuring operational reliability. This article investigates the stability switching induced by bifurcation in a fractional-order bidirectional associative memory (BAM) neural network system with higher-order interactions. First, a generalized system is formulated, featuring a complete two-layer structure comprising <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n+m$</tex-math> </inline-formula> neurons. Analytical conditions for local stability and the onset of Hopf bifurcation are derived, which are applicable to large-scale networked systems of arbitrary size. Numerical simulations validate the theoretical results and reveal rich dynamical behaviors, demonstrating that system stability and bifurcation are critically influenced by time delay, higher-order interaction strength, fractional order, and network scale. A key finding is that the proper incorporation of weak higher-order interactions can raise the bifurcation threshold and suppress oscillation amplitudes, providing theoretical guidelines for the design and optimization of complex networked systems.