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Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption

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  • Tabekoueng Njitacke, Zeric
  • Tsafack, Nestor
  • Ramakrishnan, Balamurali
  • Rajagopal, Kartikeyan
  • Kengne, Jacques
  • Awrejcewicz, Jan

Abstract

This paper studies the effect of the electromagnetic flux on the dynamics of an introduced model of heterogeneous coupled neurons. Analytical investigation of the coupled neurons revealed that the obtained model is equilibrium free thus displays hidden firing activities. Based on the Helmholtz theorem, it is demonstrated that the coupled neurons possess a Hamilton energy, which enables to keep the electrical activity of the coupled neurons. Numerical simulations based on the fourth-order Runge-Kutta formula have enabled us to find a range of the electromagnetic induction strength where the model exhibits hysteretic dynamics. That hysteresis justifies the coexistence of two different firing activities for the same parameters captured. This latter behavior is further supported using bifurcation diagrams, the graph of the maximum Lyapunov exponent, phase portraits, time series, and attraction basins as arguments. Beside, the STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed model. The results of microcontroller implementation perfectly supported the results of the numerical simulation of bistability. Finally, a compressive sensing approach is used to compress and encrypt digital images based on the sequences of the above coupled-neurons model. The plain color image is decomposed into R, G, and B components. The DWT is applied to each component to obtain the corresponding sparse components. Confusion keys are obtained from the proposed coupled neurons to scramble each sparse component. The measurement matrixes obtained from the coupled neurons sequence are used to compress the confused sparse matrices corresponding to R, G, and B components. Each component is quantified, and a diffusion step is then applied to improve the randomness and consequently the information entropy.

Suggested Citation

  • Tabekoueng Njitacke, Zeric & Tsafack, Nestor & Ramakrishnan, Balamurali & Rajagopal, Kartikeyan & Kengne, Jacques & Awrejcewicz, Jan, 2021. "Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
  • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009310
    DOI: 10.1016/j.chaos.2021.111577
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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. Njitacke, Zeric Tabekoueng & Doubla, Isaac Sami & Mabekou, Sandrine & Kengne, Jacques, 2020. "Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Lai, Qiang & Nestor, Tsafack & Kengne, Jacques & Zhao, Xiao-Wen, 2018. "Coexisting attractors and circuit implementation of a new 4D chaotic system with two equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 92-102.
    4. Bao, B. & Peol, M.A. & Bao, H. & Chen, M. & Li, H. & Chen, B., 2021. "No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Xiuli Chai & Zhihua Gan & Yang Lu & Yiran Chen & Daojun Han, 2017. "A novel image encryption algorithm based on the chaotic system and DNA computing," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(05), pages 1-24, May.
    6. Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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    Cited by:

    1. Xianhua Song & Guanglong Chen & Ahmed A. Abd El-Latif, 2022. "Quantum Color Image Encryption Scheme Based on Geometric Transformation and Intensity Channel Diffusion," Mathematics, MDPI, vol. 10(17), pages 1-23, August.
    2. Folifack Signing, V.R. & Gakam Tegue, G.A. & Kountchou, M. & Njitacke, Z.T. & Tsafack, N. & Nkapkop, J.D.D. & Lessouga Etoundi, C.M. & Kengne, J., 2022. "A cryptosystem based on a chameleon chaotic system and dynamic DNA coding," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Li, Kexin & Bao, Bocheng & Ma, Jun & Chen, Mo & Bao, Han, 2022. "Synchronization transitions in a discrete memristor-coupled bi-neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Bao, Han & Ding, Ruoyu & Chen, Bei & Xu, Quan & Bao, Bocheng, 2023. "Two-dimensional non-autonomous neuron model with parameter-controlled multi-scroll chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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