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<p>Understanding complex dynamics in neural systems is crucial for advancing neuromorphic computing and brain-inspired technologies. Conventional Tabu learning neural networks often exhibit chaotic behavior, but most existing models do not account for the simultaneous influence of multiple external electromagnetic stimuli, which is common in real biological and electronic environments. To address this gap, this paper introduces a bi-magnetized Tabu learning neural network that incorporates two enhanced memristor models to simulate the induction currents caused by dual electromagnetic radiations. We develop the mathematical model and analyze its dynamics using numerical tools such as bifurcation diagrams, Lyapunov spectra, Poincaré sections, and the 0–1 test. The study reveals a rich variety of polymorphic butterfly-shaped attractors-ranging from single-wing and double-wing to four-wing structures-that can exhibit chaotic or hyperchaotic behavior. Notably, the system also demonstrates multistability, meaning that infinitely many different attractors can coexist under the same parameters but different initial conditions. Furthermore, we design and simulate an analog electronic circuit of the proposed network using Multisim. The circuit experiments confirm the numerical predictions, verifying the physical realizability of the model. This work offers a feasible platform for studying complex neural dynamics and shows potential for applications in secure communications and neuromorphic hardware.</p>

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Polymorphic butterfly attractors in a bi-magnetized Tabu learning neural network and its analog circuit implementation

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Hairong Lin,
  • Miao Xie

摘要

Understanding complex dynamics in neural systems is crucial for advancing neuromorphic computing and brain-inspired technologies. Conventional Tabu learning neural networks often exhibit chaotic behavior, but most existing models do not account for the simultaneous influence of multiple external electromagnetic stimuli, which is common in real biological and electronic environments. To address this gap, this paper introduces a bi-magnetized Tabu learning neural network that incorporates two enhanced memristor models to simulate the induction currents caused by dual electromagnetic radiations. We develop the mathematical model and analyze its dynamics using numerical tools such as bifurcation diagrams, Lyapunov spectra, Poincaré sections, and the 0–1 test. The study reveals a rich variety of polymorphic butterfly-shaped attractors-ranging from single-wing and double-wing to four-wing structures-that can exhibit chaotic or hyperchaotic behavior. Notably, the system also demonstrates multistability, meaning that infinitely many different attractors can coexist under the same parameters but different initial conditions. Furthermore, we design and simulate an analog electronic circuit of the proposed network using Multisim. The circuit experiments confirm the numerical predictions, verifying the physical realizability of the model. This work offers a feasible platform for studying complex neural dynamics and shows potential for applications in secure communications and neuromorphic hardware.