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Dynamics of two models of driven extended jerk oscillators: Chaotic pulse generations and application in engineering

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  • Kenmogne, Fabien
  • Noubissie, Samuel
  • Ndombou, Guy Bertrand
  • Tebue, Eric Tala
  • Sonna, Armel Viquit
  • Yemélé, David

Abstract

This paper investigates the dynamics of two models of jerk equations: The first one which is very simple and driven by an external constant signal, and the second one more complicated with an external periodic excitation. These particular equations are very important mathematical models of physical systems, with broad range applications in engineering, namely in electronic and telecommunication to generate the trains of regular and chaotic pulses. Although regular pulses are useful for the modulation of signals, the chaotic one can be used for the signal masking and modulations. The simplest jerk equation is chosen in the literature, while the periodic driven one is derived from Kirchhoff laws applied on a real electronic circuit conveniently built. The existence and uniqueness of their solutions are verified from the fixed- point theorem. Particularly by using the two parameters perturbation methods usually applied to find solitons, the periodic solutions are found, and proved to be sensitive to nonlinearity parameter and the external signal voltage’s amplitudes. The numerical investigations are next performed proving the existence of some interesting results such as the bubble bifurcation and the generation of chaotic pulses. Pspice and real experiments are performed on the periodic driven version of jerk equation in order to verify theoretical investigations.

Suggested Citation

  • Kenmogne, Fabien & Noubissie, Samuel & Ndombou, Guy Bertrand & Tebue, Eric Tala & Sonna, Armel Viquit & Yemélé, David, 2021. "Dynamics of two models of driven extended jerk oscillators: Chaotic pulse generations and application in engineering," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006457
    DOI: 10.1016/j.chaos.2021.111291
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    References listed on IDEAS

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    1. Léandre Kamdjeu Kengne & Jacques Kengne & Justin Roger Mboupda Pone & Hervé Thierry Kamdem Tagne, 2020. "Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity," Complexity, Hindawi, vol. 2020, pages 1-24, April.
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    Cited by:

    1. Xia, Yibo & Hua, Shi & Bi, Qinsheng, 2023. "Quasi-periodic structure in chaotic bursting attractor for a controlled jerk oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Kenmogne, Fabien & Wokwenmendam, Martine Limi & Simo, Hervé & Adile, Adoum Danao & Noah, Pierre Marcel Anicet & Barka, Mahamat & Nguiya, Sévérin, 2022. "Effects of damping on the dynamics of an electromechanical system consisting of mechanical network of discontinuous coupled system oscillators with irrational nonlinearities: Application to sand sieve," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Rech, Paulo C., 2022. "Self-excited and hidden attractors in a multistable jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    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. Yan, Shaohui & Jiang, Defeng & Cui, Yu & Zhang, Hanbing & Li, Lin & Jiang, Jiawei, 2024. "A fractional-order hyperchaotic system that is period in integer-order case and its application in a novel high-quality color image encryption algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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