Chaotification of the Van der Pol System Using Jerk Architecture

Benitez, S.I.; Acho, Leonardo; Guerra, Ricardo J.R.

doi:10.1093/ietfec/e89-a.4.1088

Cited by 18 publications

(12 citation statements)

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“…Inspired by the works reported in Benitez et al (2006), Louodop et al (2014), Kengne et al (2016), Tamba et al (2018a) and in order to convert the second-order non-autonomous Helmholtz oscillator [see Eq. 1] to an autonomous form which can display interesting and complex features, the following model is introduced…”

Section: Analysis Of the Proposed Autonomous Helmholtz Jerk Oscillatormentioning

confidence: 99%

“…Following these ideas, development of new jerk oscillators with easy electronic implementation and the chaotification of non-chaotic oscillators, the authors of Ref. Benitez et al (2006) introduced, theoretically studied and experimented an autonomous chaotic oscillator using the Van der Pol dynamics immersed into a jerk oscillator. In Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the studies reported in Refs. Benitez et al (2006), Louodop et al (2014), Kengne et al (2016) and Tamba et al (2018a, b), in this paper we consider an autonomous jerk oscillator which is obtained by converting the second-order Helmholtz oscillator into a threedimensional oscillator using the jerk model. Helmholtz oscillator is a two-dimensional oscillator with a quadratic nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics, Circuitry Implementation and Control of an Autonomous Helmholtz Jerk Oscillator

Ainamon

Kingni

Tamba

et al. 2019

J Control Autom Electr Syst

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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.

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Section: Analysis Of the Proposed Autonomous Helmholtz Jerk Oscillatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics, Circuitry Implementation and Control of an Autonomous Helmholtz Jerk Oscillator

Ainamon

Kingni

Tamba

et al. 2019

J Control Autom Electr Syst

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“…The Van der Pol system can be performed chaotic behaviors by driving with external force [13], coupling with Duffing oscillator [14] or chaotification of the modified third order system [15]. In order to generate a hyper-chaotic attractor, a dynamic system requires the minimum number of coupled first-order autonomous ordinary differential equations to be four.…”

Section: Modified Van Der Pol Systemmentioning

confidence: 99%

Generating hyper-chaotic attractor from Van Der Pol system

Klomkarn

Payakkawan

Sooraksa

2009

2009 9th International Symposium on Communications and Information Technology

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“…However, the results of [8] are restricted on the presentation of the rate-equations of chaotic memory oscillators and make no mention on the chaotic mechanism of each MO. The authors of [9,10] introduced, theoretically studied and experimented two autonomous chaotic oscillators using the Van der Pol dynamics immersed into a jerk oscillator. These two jerk oscillators belong to the family of MO 5 .…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form

et al. 2019

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In this paper, an autonomous Toda jerk oscillator is proposed and analysed. The autonomous Toda jerk oscillator is obtained by converting an autonomous two-dimensional Toda oscillator with an exponential nonlinear term to a jerk oscillator. The existence of Hopf bifurcation is established during the stability analysis of the unique equilibrium point. For a suitable choice of the parameters, the proposed autonomous Toda jerk oscillator can generate antimonotonicity, periodic oscillations, chaotic oscillations and bubbles. By introducing two additional parameters in the proposed autonomous Toda jerk oscillator, it is possible to control partially or totally the amplitude of its signals. In addition, electronic circuit realization of the proposed Toda jerk oscillator is carried out to confirm results found during numerical simulations. The commensurate fractional-order version of the proposed autonomous chaotic Toda jerk oscillator is studied using the stability theorem of fractional-order oscillators and numerical simulations. It is found that periodic oscillations and chaos exist in the fractional-order form of the proposed Toda jerk oscillator with order less than three. Finally, combination synchronization of two fractionalorder proposed autonomous chaotic Toda jerk oscillators with another fractional-order proposed autonomous chaotic Toda jerk oscillator is analysed using the nonlinear feedback control method.

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Chaotification of the Van der Pol System Using Jerk Architecture

Cited by 18 publications

References 0 publications

Dynamics, Circuitry Implementation and Control of an Autonomous Helmholtz Jerk Oscillator

Dynamics, Circuitry Implementation and Control of an Autonomous Helmholtz Jerk Oscillator

Generating hyper-chaotic attractor from Van Der Pol system

Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form

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