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Regime transition and multi-scroll hyperchaos in a discrete neuron model

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Abstract

Most discrete neuron models have simple algebraic structures with easy digital implementation. However, they cannot show the abundant firing regimes of neurons. To address this issue, in this paper, we propose an improved discrete tabu learning neuron (IDTLN) model using sine nonlinearity as the activation function. Using this model, the fixed points and their stability are analyzed theoretically, the parameter-related bifurcation and regime transition behaviors as well as heterogeneous multistability are investigated by numerical tools, and the multi-scroll hyperchaotic behaviors are revealed according to the dynamics distribution in the parameter plane. It is shown that the IDTLN model has two types of fixed points, stable and unstable, and their number and stability types change with the parameters, which leads to the formation of multistability and the generation of multi-scroll hyperchaotic attractors. Besides, we design six pseudorandom number generators (PRNGs) using multi-scroll hyperchaotic sequences provided by the IDTLN model and evaluate their randomness using TestU01. The evaluation results show that this proposed neuron model has high randomness without chaos degradation, which is particularly suitable for PRNG application. Finally, we develop a digital hardware platform to verify the regime transition and multi-scroll hyperchaos of the IDTLN model.

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Data availability

The data used in this research work are available from the authors by reasonably request.

Notes

  1. http://simul.iro.umontreal.ca/testu01/tu01.html.

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Funding

This work was supported by the National Natural Science Foundation of China under Grant Nos. 62271088, 62201094, and 52277001, 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, Zhuowu Wang, Mo Chen & Han Bao

  2. School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, Shenzhen, 518055, China

    Zhongyun Hua

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  1. Bocheng Bao
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Correspondence to Han Bao.

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Bao, B., Wang, Z., Hua, Z. et al. Regime transition and multi-scroll hyperchaos in a discrete neuron model. Nonlinear Dyn 111, 13499–13512 (2023). https://doi.org/10.1007/s11071-023-08543-2

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