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<p>In previous studies on the bifurcation analysis of neural networks, the precise relationship between dynamic bifurcation and system parameters has often remained unclear. This paper investigates the dynamic bifurcation and control of delayed fractional-order bidirectional associative memory inertial neural networks (FOBAMINNs). First, the stability of the FOBAMINNs without delay is analyzed by examining the corresponding characteristic equations. Then, its dynamics with delay, which is taken as the bifurcation parameter, is studied. Sufficient conditions for delay-induced Hopf bifurcation are established. Consequently, an explicit analytical formula is derived to elucidate the relationship between the bifurcation point and system parameters. To effectively control the dynamic bifurcation, a feedback controller is designed. Theoretical analysis demonstrates that the emergence of bifurcation points can be effectively delayed by appropriately selecting the feedback control gain. Simulation results confirm the validity of the main results.</p>

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Bifurcation and stabilization of a class of delayed fractional-order bidirectional associative memory inertia neural networks

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Heng Liu,
  • Jiajie Jiang,
  • Quanbao Ji,
  • Jinde Cao,
  • Chengdai Huang

摘要

In previous studies on the bifurcation analysis of neural networks, the precise relationship between dynamic bifurcation and system parameters has often remained unclear. This paper investigates the dynamic bifurcation and control of delayed fractional-order bidirectional associative memory inertial neural networks (FOBAMINNs). First, the stability of the FOBAMINNs without delay is analyzed by examining the corresponding characteristic equations. Then, its dynamics with delay, which is taken as the bifurcation parameter, is studied. Sufficient conditions for delay-induced Hopf bifurcation are established. Consequently, an explicit analytical formula is derived to elucidate the relationship between the bifurcation point and system parameters. To effectively control the dynamic bifurcation, a feedback controller is designed. Theoretical analysis demonstrates that the emergence of bifurcation points can be effectively delayed by appropriately selecting the feedback control gain. Simulation results confirm the validity of the main results.