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Burst patterns with Hopf bifurcation in a simplified FHN circuit

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Abstract

To theoretically and experimentally characterize the neuronal burst patterns, a simplified FitzHugh–Nagumo (FHN) circuit is developed by using two anti-parallel diodes to achieve nonlinearity, and its non-autonomous system model is thereby built. The simplified FHN system has a time-varying equilibrium point, whose position and stability change slowly over time. By employing numerical measures, periodic and quasi-periodic burst patterns along with quasi-periodic spike patterns are revealed in the simplified FHN system. Particularly, through constructing Hopf bifurcation set, the bifurcation mechanism for the burst behaviors is expounded theoretically. As a result, transitions between the spike and resting states are demonstrated, and Hopf/Hopf periodic and quasi-periodic burst patterns are identified. Finally, with the developed Multisim simulation model, analog circuit simulations and breadboard experiments are performed to confirm numerical results. Notably, the simplified FHN circuit is implemented with low-cost and no multiplier, which is of great significance for the construction of neuromorphic systems and contributes to the research and development of artificial neural networks.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundations of China under Grant No. 62201094, Grant No. 62271088, and Grant No. 12172066, and the Scientific Research Foundation of Jiangsu Provincial Education Department, China, under Grant No. 22KJB510001.

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Authors and Affiliations

  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159, China

    Bocheng Bao, Liuhui Chen, Han Bao, Quan Xu, Mo Chen & Huagan Wu

Authors
  1. Bocheng Bao
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  2. Liuhui Chen
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  3. Han Bao
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  4. Quan Xu
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  5. Mo Chen
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  6. Huagan Wu
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Contributions

B. C. Bao: Methodology, Formal analysis, Writing - original draft. L. H. Chen: Conceptualization, Formal analysis, Investigation. H. Bao: Formal analysis, Writing - review & editing. Q. Xu: Supervision. M. Chen: Software. H. G. Wu: Project administration Writing, - review & editing.

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Correspondence to Han Bao.

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Bao, B., Chen, L., Bao, H. et al. Burst patterns with Hopf bifurcation in a simplified FHN circuit. Nonlinear Dyn 112, 10373–10390 (2024). https://doi.org/10.1007/s11071-024-09612-w

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