Practical finite-time synchronization of jerk systems: Theory and experiment

Louodop, Patrick; Kountchou, Michaux; Fotsin, Hilaire Bertrand; Bowong, Samuel

doi:10.1007/s11071-014-1463-5

Cited by 63 publications

(28 citation statements)

References 23 publications

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“…Hence, it clearly appears that the synchronization time has to be known and minimized, so to make the synchronization be achieved as fast as possible. In this context, there is a relentless activity in the study of finite-time chaos synchronization [36,37] and gradually of fractional-order systems [38][39][40]. Unfortunately, in many of these references dealing with synchronization, for example in the previous three, applications in secure communication are missing.…”

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

et al. 2017

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Abstract. The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractionalorder systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.

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Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

et al. 2017

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“…In this work, we consider a simple jerk system with hyperbolic tangent nonlinearity [18] whose symmetry is broken by the introduction of an additive constant k. We address the chaos generation mechanism, the formation of bubbles of bifurcation, and the coexistence of multiple attractors in both the symmetric (k � 0) and the asymmetric (k ≠ 0) regimes of operation. For convenience, recall that jerk dynamic systems [19][20][21][22][23] refer to 3D ordinary differential equations (ODEs) in the form x ... � J(x, _ x, € x) where the nonlinear vector function J(·) indicates the "jerk" (i.e., the time derivative of the acceleration). e hyperbolic tangent function is relevant in numerous problems such as nonideal operational amplifiers, activation function in neural network, magnetization in ferromagnetic systems, and solar wind-driven magnetosphere-ionosphere systems [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity

Kengne

Pone

et al. 2020

Complexity

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Symmetry is an important property found in a large number of nonlinear systems. The study of chaotic systems with symmetry is well documented. However, the literature is unfortunately very poor concerning the dynamics of such systems when their symmetry is altered or broken. In this paper, we investigate the dynamics of a simple jerk system with hyperbolic tangent nonlinearity (Kengne et al., Chaos Solitons, and Fractals, 2017) whose symmetry is broken by adding a constant term modeling an external excitation force. We demonstrate that the modified system experiences several unusual and striking nonlinear phenomena including coexisting bifurcation branches, hysteretic dynamics, coexisting asymmetric bubbles, critical transitions, and multiple (i.e., up to six) coexisting asymmetric attractors for some suitable ranges of system parameters. These features are highlighted by exploiting common nonlinear analysis tools such as graphs of largest Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction. The control of multistability is investigated by using the method of linear augmentation. We demonstrate that the multistable system can be converted to a monostable state by smoothly adjusting the coupling parameter. The theoretical results are confirmed by performing a series of PSpice simulations based on an electronic analogue of the system.

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“…A common feature in this literature is that the convergence is achieved with two systems of equations using various control methods with kernel being based on the system state variables as usually applied on nonlinear circuits. 2,[8][9][10][11][12][13][14][15][16][17] However, with this approach the control error is not accurate enough because it is subject to either chattering phenomenon or the closeness to initial conditions. This led scientists to develop new approaches.…”

Section: Introductionmentioning

confidence: 99%

Simple finite-time sliding mode control approach for jerk systems

Nguazon

Nguekeng

Tchitnga

et al. 2019

Advances in Mechanical Engineering

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This article describes an easy way to apply active control upon all jerk systems for which the linear part of the thirdorder differential jerk equation strongly depends on acceleration and velocity. The kernel of that methodology is to rewrite the jerk equation as a single implicit first-order differential equation escorted with a sliding variable. It is shown that, for such a jerk class, the fast terminal sliding convergence based on Lyapunov stability is achieved with a first-order sigmoid sliding surface. Various numerical simulations have been conducted on Sprott simple jerk class as well as on the single op-amp jerk system. For experiment, we synchronize two Sprott circuits with nonlinearity being the absolute value of position. Experimental results match well with numerical simulations.

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Practical finite-time synchronization of jerk systems: Theory and experiment

Cited by 63 publications

References 23 publications

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity

Simple finite-time sliding mode control approach for jerk systems

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