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The effects of symmetry breaking on the dynamics of an inertial neural system with a non-monotonic activation function: Theoretical study, asymmetric multistability and experimental investigation

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  • Boui A Boya, Bertrand Frederick
  • Ramakrishnan, Balamurali
  • Effa, Joseph Yves
  • Kengne, Jacques
  • Rajagopal, Karthikeyan

Abstract

Multistability and symmetry breaking have been significantly investigated recently. In this paper, we study the effects of symmetry breaking on the behavior of a particular class of inertial neural systems with a non-monotonic activation function. By introducing a constant term in the nonlinearity of the model, we show that this system presents asymmetric type dynamics marked by the coexistence of chaotic bursting oscillations according to the different membranes of the neurons. We also report some interesting phenomena such as rising voltage peaks, the coexistence of several asymmetric attractors (six, five, four and three), the coexistence of asymmetric bubbles of bifurcation and transient chaos as well. We illustrate the influence of the symmetry breaking parameter by using 2D Lyapunov exponent, plotted for three different values of the symmetry control parameter. We prove that this model owns offset boosting and total amplitude control features. The experimental study is executed based on a microcontroller implementation and the results are in agreement with the numerical analysis.

Suggested Citation

  • Boui A Boya, Bertrand Frederick & Ramakrishnan, Balamurali & Effa, Joseph Yves & Kengne, Jacques & Rajagopal, Karthikeyan, 2022. "The effects of symmetry breaking on the dynamics of an inertial neural system with a non-monotonic activation function: Theoretical study, asymmetric multistability and experimental investigation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    • Handle: RePEc:eee:phsmap:v:602:y:2022:i:c:s0378437122003351
    DOI: 10.1016/j.physa.2022.127458
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    References listed on IDEAS

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    1. Megam Ngouonkadi, E.B. & Fotsin, H.B. & Louodop Fotso, P. & Kamdoum Tamba, V. & Cerdeira, Hilda A., 2016. "Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 151-163.
    2. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    3. Xu, Quan & Tan, Xiao & Zhu, Dong & Bao, Han & Hu, Yihua & Bao, Bocheng, 2020. "Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Chen, Chengjie & Min, Fuhong & Zhang, Yunzhen & Bao, Han, 2023. "ReLU-type Hopfield neural network with analog hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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