Experimental Observations and Circuit Realization of a Jerk Chaotic System With Piecewise Nonlinear Function

Lassoued, Abir; Boubaker, Olfa; Dhifaoui, Rachid; Jafari, Sajad

doi:10.1016/b978-0-12-815838-8.00001-7

Cited by 9 publications

(5 citation statements)

References 20 publications

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“…Deterministic chaos is a typical phenomenon for nonlinear dynamical system such as Lotka-Volterra model. The Lyapunov exponent (LE) is the principal criteria for characterizing chaotic behaviour of dynamical system ( Lassoued et al, 2019 , Açıkgöz et al, 2020 , Othman et al, 2019 ). The LE detects the presence of chaos and quantifies the stability of the dynamical system.…”

Section: Port Interactions and Dynamical Analysismentioning

confidence: 99%

Seaport throughput forecasting and post COVID-19 recovery policy by using effective decision‐making strategy: A case study of Vietnam ports

Cuong

Kim

You

et al. 2022

Computers & Industrial Engineering

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Section: Port Interactions and Dynamical Analysismentioning

confidence: 99%

Seaport throughput forecasting and post COVID-19 recovery policy by using effective decision‐making strategy: A case study of Vietnam ports

Cuong

Kim

You

et al. 2022

Computers & Industrial Engineering

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“…The critical nature of the chaotic attractor means that the value of Lyapunov exponent approaches zero. 16 The mathematical model of largest Lyapunov exponent is as below…”

Section: Nonlinear Dynamic Response For the Followermentioning

confidence: 99%

Nonlinear dynamics behavior of cam-follower system using concave curvatures profile

Yousuf

Marghitu

2020

Advances in Mechanical Engineering

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Nonlinear dynamics behavior of the roller follower is discussed for different follower guides’ internal dimensions and cam angular speeds. A dynamic tool such as Wolf algorithm is used to extract largest Lyapunov exponent parameter. Positive value of Lyapunov exponent parameter indicates non-periodic motion and chaos. The influence of flank curvature of the cam profile on the nonlinear dynamic behavior of the roller follower is investigated. Impulse and momentum theory is used to describe the impact phenomenon based on the contact force between the follower and its guides. Contact parameters such as exponent, sliding contact velocity, contact bodies stiffness, penetration, and damping ratio are used in SolidWorks software to simulate follower movement numerically. Experiment setup has been done by taking into consideration the use of an infrared three-dimensional camera device through a high precision optical sensor. The follower motion is non-periodic when the cross-linking of phase-plane diagram diverges with no limit of spiral cycles.

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“…Intensive and repetitive simulations are also needed to study particular phenomena such as bifurcations [9,10] and chaos [10,11]. It is shown in the literature that a lot of piecewise dynamic systems exhibit chaotic behaviour [12,13]. DC-DC converters are nonlinear periodically controlled systems that operate under practically piecewise dynamic trajectories.…”

Section: Introductionmentioning

confidence: 99%

“…e second goal of the paper is to use these results in developing a discrete iterative map formulated as in standard discrete time series models [15,16]. A Jacobian matrix as found with an iterative map is defined and used to compute Lyapunov exponents [12,13] via the QR factorisation technique.…”

Section: Introductionmentioning

confidence: 99%

Fast Simulation and Chaos Investigation of a DC-DC Boost Inverter

Dhifaou

Brahmi

2021

Complexity

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Intensive and repetitive simulations are required to study static and dynamic behaviours of systems. Particular phenomena such as bifurcation and chaos require long simulation times and analysis. To check the existence of bifurcations and chaos in a dynamic system, a fine-tuning procedure of a bifurcation parameter is to be carried out. This increases considerably the computing time, and a great amount of patience is needed to obtain adequate results. Because of the high switching frequency of a boost inverter, the integration process of the dynamic model used to describe it uses an integration step that is in general less than one microsecond. This makes the integration process time consuming even for a short simulation. Thus, a fast, but accurate, method is suitable to analyse the dynamic behaviour of the converter. This work contains two topics. First, we develop a like-discrete integration process that permits precise results in a very fast manner. For one switching period, we compute only two or a maximum of three breaking points depending on whether we treat a continuous conduction mode (CCM) or a discontinuous conduction mode (DCM) of the inductor current. Furthermore, with each segment of the dynamic trajectory, an exact analytic formula is associated. The second goal is to use this result to develop a discrete iterative map formulated as in standard discrete time series models. The Jacobian matrix of the found iterative map is defined and used to compute Lyapunov exponents to prove existence of chaos. Performance of the developed study is positively evaluated by using classical simulations and fine-tuning a bifurcation parameter to detect chaos. This parameter is the desired reference of the inductor current peak. Results show that the proposed scheme is very fast and accurate. The study can be easily extended to other switching topologies of DC-DC inverters.

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Experimental Observations and Circuit Realization of a Jerk Chaotic System With Piecewise Nonlinear Function

Cited by 9 publications

References 20 publications

Seaport throughput forecasting and post COVID-19 recovery policy by using effective decision‐making strategy: A case study of Vietnam ports

Seaport throughput forecasting and post COVID-19 recovery policy by using effective decision‐making strategy: A case study of Vietnam ports

Nonlinear dynamics behavior of cam-follower system using concave curvatures profile

Fast Simulation and Chaos Investigation of a DC-DC Boost Inverter

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