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

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

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

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.

Keywords: Non-autonomous oscillator; Jerk chaotic oscillator; Train of chaotic pulse; Approximated Solution (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006457

DOI: 10.1016/j.chaos.2021.111291

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