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<p>The diversification of attractor structures and their programmable regulation represent a significant direction in neural network dynamics. However, conventional memristive Hopfield neural networks (MHNNs) are often limited by symmetry, which restricts structural diversity and adaptive control. To overcome this, a programmable memristive Hopfield neural network (MP-HNN) is proposed. The programmability is realized by introducing a memristor switchable among three modes (odd, even, and increasing functions), through which the controllable expansion of the number of equilibrium points and the flexible configuration of the attractor structure are enabled. Under the increasing function mode, an asymmetric distribution of equilibrium points is generated, effectively breaking the traditional symmetric constraint. This paper systematically analyzes the equilibrium distribution, stability, and bifurcation behavior of the MP-HNN, and examines attractor evolution under different functional modes. Results show that coordinated parameter adjustment allows the network to produce double-scroll attractors and simulate neural firing patterns such as periodic and chaotic bursting. Significant synchronization is also observed between system state variables and memristor flux. Finally, FPGA-based hardware implementation closely matches numerical simulations, validating the model and theoretical analysis.</p>

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Multi-scroll regulation and control of a programmable memristive Hopfield neural network with FPGA implementation

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Xiangcong Wu,
  • Suo Gao,
  • Herbert Ho-Ching Iu,
  • Junxin Chen,
  • Yushu Zhang,
  • Yinghong Cao,
  • Jun Mou

摘要

The diversification of attractor structures and their programmable regulation represent a significant direction in neural network dynamics. However, conventional memristive Hopfield neural networks (MHNNs) are often limited by symmetry, which restricts structural diversity and adaptive control. To overcome this, a programmable memristive Hopfield neural network (MP-HNN) is proposed. The programmability is realized by introducing a memristor switchable among three modes (odd, even, and increasing functions), through which the controllable expansion of the number of equilibrium points and the flexible configuration of the attractor structure are enabled. Under the increasing function mode, an asymmetric distribution of equilibrium points is generated, effectively breaking the traditional symmetric constraint. This paper systematically analyzes the equilibrium distribution, stability, and bifurcation behavior of the MP-HNN, and examines attractor evolution under different functional modes. Results show that coordinated parameter adjustment allows the network to produce double-scroll attractors and simulate neural firing patterns such as periodic and chaotic bursting. Significant synchronization is also observed between system state variables and memristor flux. Finally, FPGA-based hardware implementation closely matches numerical simulations, validating the model and theoretical analysis.