https://doi.org/10.1140/epjp/s13360-024-05046-w
Regular Article
Periodic firing evolution of a Hindmarsh–Rose neuron model and FPGA circuit implementation
1
School of Mechanical Engineering, Northwestern Polytechnical University, 710072, Xi’an, People’s Republic of China
2
China Aerodynamics Research and Development Center, P.O.Box 211, 621000, Mianyang, People’s Republic of China
Received:
21
December
2023
Accepted:
27
February
2024
Published online:
11
March
2024
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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
