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Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation

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  • Dlamini, A.
  • Doungmo Goufo, E.F.

Abstract

The concept of self-similarity, widely employed in specialized fields of applied sciences, has been investigated through numerous works utilizing both analytical elements and experimental observations. As a significant component of both fractal and chaos theories, self-similarity can naturally manifest around us or be artificially simulated using mathematical arguments and algorithms. In this paper, we utilize analytical, numerical, and experimental circuit elements to study, analyze, and simulate a generalized chaotic system of attractors with multiple scrolls. This system presents various types of processes, including chaotic and hyperchaotic dynamics, as well as hidden attractors. We discuss the well-posedness of the system before examining its numerical solvability, error tolerance, and simulations for the model involving fractal and fractional operations. Simulations are conducted for various values of the model’s parameters, demonstrating that the system displays fractal features combined with chaotic behavior. The system is implemented using a Field Programmable Gate Array (FPGA) board, generating self-similar results akin to those obtained numerically.

Suggested Citation

  • Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923009852
    DOI: 10.1016/j.chaos.2023.114084
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    1. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    2. A. Dlamini & Emile F. Doungmo Goufo & M. Khumalo, 2022. "Chaotic Behavior Of Modified Stretch–Twist–Fold Flow Under Fractal-Fractional Derivatives," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-30, December.
    3. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    4. Njitacke, Z.T. & kengne, J. & Kengne, L. Kamdjeu, 2017. "Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 77-91.
    5. Jahanshahi, Hadi & Orozco-López, Onofre & Munoz-Pacheco, Jesus M. & Alotaibi, Naif D. & Volos, Christos & Wang, Zhen & Sevilla-Escoboza, R. & Chu, Yu-Ming, 2021. "Simulation and experimental validation of a non-equilibrium chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. 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).
    7. Bouallegue, Kais & Chaari, Abdessattar & Toumi, Ahmed, 2011. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 79-85.
    8. Yan, Dengwei & Wang, Lidan & Duan, Shukai & Chen, Jiaojiao & Chen, Jiahao, 2021. "Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Nasr, Salah & Mekki, Hassen & Bouallegue, Kais, 2019. "A multi-scroll chaotic system for a higher coverage path planning of a mobile robot using flatness controller," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 366-375.
    10. Emile F. Doungmo Goufo & Y. Khan & I. Tchangou Toudjeu, 2022. "The Fractal And Piecewise Structure Of Some Chaotic Neural Networks Using A Generalized Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-19, December.
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