Dynamics, Circuitry Implementation and Control of an Autonomous Helmholtz Jerk Oscillator
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Date
2019-03-21
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Link
Abstract
In this paper, an autonomous three-dimensional Helmholtz-type oscillator is designed based on conversion of an autonomous Helmholtz two-dimensional oscillator to a jerk oscillator. For a suitable choice of the parameters, the proposed autonomous Helmholtz jerk oscillator can generate Hopf bifurcation, bistable period-2 limit cycles, two types of one-scroll chaotic attractors and coexistence between period-3 limit cycle and one-scroll chaotic attractors. Using a weak modulation of a parameter of the proposed Helmholtz jerk oscillator, it is possible to destroy the coexisting attractors found and transform the proposed Helmholtz jerk oscillator to period-3 oscillations. Moreover using experiments and OrCAD-PSpice software, circuit implementation of the proposed autonomous Helmholtz jerk oscillator is realized in order to check the one-scroll chaotic attractors and the coexisting attractors found during the numerical simulations. Numerical and experimental/OrCAD-PSpice results have a good qualitative agreement. Finally, by adding two new parameters in the proposed autonomous Helmholtz jerk oscillator, it is possible to control the amplitude of the attractor and the largest Lyapunov exponent.
Description
Chaotic behavior in nonlinear oscillators has been investigated in the past four decades, but the systems considered lead to difficult electronic implementations. Since 2000, the
development of new autonomous chaotic oscillators with easy electronic implementation has been of interest, as it can be seen in Sprott papers (Sprott 2000a, b).
Keywords
Helmholtz jerk oscillator, Hopf bifurcation, Chaos, Coexistence of attractors and its control, Electronic circuit realization, Amplitude and Lyapunov exponent control
Citation
Ainamon, C., Kingni, S.T., Tamba, Tamba, V.K., Orou, J.B.C., Woafo, P. (2019). Dynamics, Circuitry Implementation and Control of an Autonomous Helmholtz Jerk Oscillator. Journal of Control, Automation and Electrical Systems https://doi.org/10.1007/s40313-019-00463-0