A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

Tchitnga, Robert; Nanfa'a, R. Zebaze; Pelap, F. B.; Louodop, Patrick; Woafo, P.

doi:10.1177/1077546315585424

Cited by 12 publications

(14 citation statements)

References 18 publications

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“…Recent examples of two-component electronic circuits [41] operating at high frequency [42,43] have been reported. In spite of the simplicity of [43] made solely of a transistor and a tapped coil, Joana et al [44] have revealed the presence of infinite families of spiral phases of stability in its phase diagrams.…”

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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“…are the corresponding finite times of the usual Lyapunov function derivative. The inequality in equation (27) is derived by integrating the relations in equations (21) and (22).…”

Section: Ftsm Synchronization Of Two Circuits Encoded By An Implicit mentioning

confidence: 99%

“…26 The aim of this section is to achieve the fast finite-time synchronization of two similar systems described by equation ( 1) using a nonlinear sliding surface of the implicit variable g. The nonlinearity of the controller is based on sigmoid function. 27 Generally, the sigmoid function is used in the SMC method to achieve asymptotical convergence of the controlled systems. 2,3,10,11,13,[18][19][20][21][22][23][24][25][26][27][28][29] However, with the advantages offered by jerk equations, the FTSM convergence can be obtained if the sigmoid function is a hyperbolic tangent function.…”

Section: Ftsm Synchronization Of Two Circuits Encoded By An Implicit Equationmentioning

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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“…One of the most active fields for chaos and applications remains that of electronic circuits. Apart from the groundbreaking Chua's circuit [3], many other chaotic circuits have been found, or existing oscillators used to introduce sinusoidal oscillations in curricula have been modified for chaos [16, 17, 18, 19, 20, 21], so that proposing new circuits can now make sense according to Sprott [22], only if they fulfill at least one of the following requirements:Credibly modeling some important unsolved problem in nature and shed insight on that problem;Exhibiting some behavior previously unobserved orBeing simpler than all other known examples exhibiting the observed behavior.…”

Section: Introductionmentioning

confidence: 99%

Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity

Talla

Tchitnga

Kengne

et al. 2019

Heliyon

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A simple driven bipolar junction transistor (BJT) based two-component circuit is presented, to be used as didactic tool by Lecturers, seeking to introduce some elements of complex dynamics to undergraduate and graduate students, using familiar electronic components to avoid the traditional black-box consideration of active elements. Although the effect of the base-emitter (BE) junction is practically suppressed in the model, chaotic phenomena are detected in the circuit at high frequencies (HF), due to both the reactant behavior of the second component, a coil, and to the birth of parasitic capacitances as well as to the effect of the weak nonlinearity from the base-collector (BC) junction of the BJT, which is otherwise always neglected to the favor of the predominant but now suppressed base-emitter one. The behavior of the circuit is analyzed in terms of stability, phase space, time series and bifurcation diagrams, Lyapunov exponents, as well as frequency spectra and Poincaré map section. We find that a limit cycle attractor widens to chaotic attractors through the splitting and the inverse splitting of periods known as antimonotonicity. Coexisting bifurcations confirm the existence of multi-stability behaviors, marked by the simultaneous apparition of different attractors (periodic and chaotic ones) for the same values of system parameters and different initial conditions. This contribution provides an enriching complement in the dynamics of simple chaotic circuits functioning at high frequencies. Experimental lab results are completed with PSpice simulations and theoretical ones.

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A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

Cited by 12 publications

References 18 publications

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

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

Simple finite-time sliding mode control approach for jerk systems

Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity

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