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<p>We propose a three-neuron heterogeneous cyclic Hopfield neural network (het-CHNN) utilizing three different activation functions: the hyperbolic tangent, sine, and cosine functions. The network’s globally uniformly ultimate boundedness is proved theoretically, and its chaotic dynamics are explored through numerical simulations and analog experiments. The numerical results demonstrate that the het-CHNN displays chaotic dynamics and multi-scroll chaotic attractors. Subsequently, the het-CHNN is implemented in an analog circuit, and hardware experiments are performed to verify the previous numerical results. Notably, the het-CHNN successfully resolves the issue of the absence of chaos in a three-neuron CHNN and currently appears to be the simplest three-neuron Hopfield neural network (HNN) that can generate chaos.</p>

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A heterogeneous cyclic Hopfield neural network without self-connections

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Yunzhen Zhang,
  • Chunlong Zhou,
  • Han Bao,
  • Guangzhe Zhao,
  • Bocheng Bao

摘要

We propose a three-neuron heterogeneous cyclic Hopfield neural network (het-CHNN) utilizing three different activation functions: the hyperbolic tangent, sine, and cosine functions. The network’s globally uniformly ultimate boundedness is proved theoretically, and its chaotic dynamics are explored through numerical simulations and analog experiments. The numerical results demonstrate that the het-CHNN displays chaotic dynamics and multi-scroll chaotic attractors. Subsequently, the het-CHNN is implemented in an analog circuit, and hardware experiments are performed to verify the previous numerical results. Notably, the het-CHNN successfully resolves the issue of the absence of chaos in a three-neuron CHNN and currently appears to be the simplest three-neuron Hopfield neural network (HNN) that can generate chaos.