Periodic firing evolution of a Hindmarsh–Rose neuron model and FPGA circuit implementation

The discrete mapping method is used to study the firing trajectory of a 3D Hindmarsh–Rose model with periodic excitation. By constructing a discrete 3D Hindmarsh Rose model, the implicit mapping relationships are obtained. Then, the Period-Doubling, Saddle-Node, and Neimark bifurcations of Hindmarsh...

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Bibliographic Details
Published in:European physical journal plus 2024-03, Vol.139 (3), p.235, Article 235
Main Authors: Liu, Yan, Shen, Yingjie, Zhang, Haowei, Li, Zhihui
Format: Article
Language:English
Subjects:
Accuracy
Applied and Technical Physics
Atomic
Bifurcations
Complex Systems
Condensed Matter Physics
Eigenvalues
Excitation
Mapping
Mathematical and Computational Physics
Mathematical models
Molecular
Neural networks
Neurons
Optical and Plasma Physics
Parameters
Physics
Physics and Astronomy
Radiation
Regular Article
Theoretical
Three dimensional models
Waveforms
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Summary:The discrete mapping method is used to study the firing trajectory of a 3D Hindmarsh–Rose model with periodic excitation. By constructing a discrete 3D Hindmarsh Rose model, the implicit mapping relationships are obtained. Then, the Period-Doubling, Saddle-Node, and Neimark bifurcations of Hindmarsh–Rose neurons from periodic motion to chaos with periodic excitation are analyzed. With the excitation changing, the Hindmarsh–Rose model exhibits dynamic bifurcation characteristics correspondingly, and a single or multiple firing activities appear in a single periodic motion. Furthermore, the effects of the amplitude and frequency of periodic excitation are described to reveal the stability region of the model, and the existence range of independent and continuous periodic motion in the two-parameter graph is found. Finally, by optimizing and adjusting parameters, a corresponding FPGA circuit is constructed to achieve the periodic firing characteristics. The result shows that waveform of the FPGA circuit match well with the theoretical results.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-024-05046-w