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Finite-time divergence in Chialvo hyperneuron model of nilpotent matrices

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  • Smidtaite, Rasa
  • Ragulskis, Minvydas

Abstract

The Chialvo hyperneuron model is introduced as the extension of the scalar Chialvo neuron model in this paper. The complexity of the model is increased not by adding another spatial variable but by replacing scalar nodal variables with square matrices of iterative variables. It is shown that such an extension does yield the effect of the divergence if the matrices of iterative variables are nilpotent matrices and the Lyapunov exponent of the scalar Chialvo neuron model is positive. Different regimes of divergence are classified into the finite-time and the explosive divergence of the hyperneuron. Analytical and computational simulations are used to illustrate the complex dynamical behavior of the Chialvo hyperneuron not observable in the scalar Chialvo neuron model.

Suggested Citation

  • Smidtaite, Rasa & Ragulskis, Minvydas, 2024. "Finite-time divergence in Chialvo hyperneuron model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s096007792400033x
    DOI: 10.1016/j.chaos.2024.114482
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    References listed on IDEAS

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    1. Rasa Smidtaite & Jurate Ragulskiene & Liepa Bikulciene & Minvydas Ragulskis & Jesus M. Munoz-Pacheco, 2023. "Hyper Coupled Map Lattices for Hiding Multiple Images," Complexity, Hindawi, vol. 2023, pages 1-20, July.
    2. Lu, Guangqing & Smidtaite, Rasa & Navickas, Zenonas & Ragulskis, Minvydas, 2018. "The Effect of Explosive Divergence in a Coupled Map Lattice of Matrices," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 308-313.
    3. Zandi-Mehran, Nazanin & Panahi, Shirin & Hosseini, Zahra & Hashemi Golpayegani, Seyed Mohammad Reza & Jafari, Sajad, 2020. "One dimensional map-based neuron model: A phase space interpretation," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Muni, Sishu Shankar & Rajagopal, Karthikeyan & Karthikeyan, Anitha & Arun, Sundaram, 2022. "Discrete hybrid Izhikevich neuron model: Nodal and network behaviours considering electromagnetic flux coupling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Jing, Zhujun & Yang, Jianping & Feng, Wei, 2006. "Bifurcation and chaos in neural excitable system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 197-215.
    6. Lu, Guangqing & Smidtaite, Rasa & Howard, Daniel & Ragulskis, Minvydas, 2019. "An image hiding scheme in a 2-dimensional coupled map lattice of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 78-85.
    7. Smidtaite, Rasa & Ragulskis, Minvydas, 2022. "Spiral waves of divergence in the Barkley model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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