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<p>This study develops a simple second-order RC oscillator-based neuron circuit. By establishing its non-autonomous piecewise linear neuron model, the equilibrium state and stability are discussed, the chaotic dynamics and coexisting oscillations are explored, and the periodic bursting and quasi-periodic spiking oscillations are disclosed. Particularly, the stability transition of the equilibrium state in a full bursting cycle triggers the boundary&#xa0;equilibrium bifurcation, resulting in periodic bursting oscillations. To elucidate the bifurcation mechanism, the switching between the spiking state and the resting state is demonstrated, and the periodic bursting oscillations induced by the boundary&#xa0;equilibrium bifurcation are confirmed. Besides, PSIM simulations are carried out by constructing circuit simulation model, and analog experiments are performed by fabricating printed circuit board hardware circuit. Both results validate the numerical findings well.</p>

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Coexisting and bursting oscillations in a second-order RC-oscillator-based piecewise linear neuron circuit

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • Bei Chen,
  • Yibo Liu,
  • Han Bao,
  • Xi Zhang,
  • Bocheng Bao

摘要

This study develops a simple second-order RC oscillator-based neuron circuit. By establishing its non-autonomous piecewise linear neuron model, the equilibrium state and stability are discussed, the chaotic dynamics and coexisting oscillations are explored, and the periodic bursting and quasi-periodic spiking oscillations are disclosed. Particularly, the stability transition of the equilibrium state in a full bursting cycle triggers the boundary equilibrium bifurcation, resulting in periodic bursting oscillations. To elucidate the bifurcation mechanism, the switching between the spiking state and the resting state is demonstrated, and the periodic bursting oscillations induced by the boundary equilibrium bifurcation are confirmed. Besides, PSIM simulations are carried out by constructing circuit simulation model, and analog experiments are performed by fabricating printed circuit board hardware circuit. Both results validate the numerical findings well.