Hartley’s oscillator: The simplest chaotic two-component circuit

Tchitnga, Robert; Fotsin, Hilaire Bertrand; Nana, B.; Louodop, Patrick; Woafo, P.

doi:10.1016/j.chaos.2011.12.017

Cited by 68 publications

(61 citation statements)

References 27 publications

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“…This memory modifies effective dimensionality of the dynamical system. [43], using the simplified Giacoletto dynamic model of the JFET for small signals at high frequency and governed by the fractional-order four-dimensional flow in equation (1). Figure 1 represents the high-frequency small-signal equivalent model of the two-component oscillator modeled by Tchitnga et al in [43].…”

Section: Circuit Model and Mathematical Modelingmentioning

confidence: 99%

“…In the present paper, based on the Lyapunov function a fractional adaptive finite-time synchronization reflecting the method in [47] is proposed for fractional-order versions of the circuit in [43]. Then, a new key system for encryption on digital cryptography is found, using the proposed finite-time synchronization scheme which is more secure and more powerful than an existing key system of integerorder synchronization [22].…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…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. Meanwhile Nguimdo et al [45] coupling three such circuits in a unidirectional ring studied with success their potential applications to random bit generator.…”

Section: Introductionmentioning

confidence: 99%

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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: Circuit Model and Mathematical Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…In this paper, the method has been applied to certain nonlinear RLC circuit systems that are closely related to nonlinear oscillation [7], electronic theory (the differential equation of self-excited oscillation of an electronic triode [8]), and Lienard and Van der Pol equations. One can find some beautiful works in the literature discussing the stability (instability) behavior of circuit systems, such as Lyapunov stability for nonlinear descriptor systems [9], the global qualitative behavior of the double scroll system [10], chaos in the Colpitts oscillator due to positive Lyapunov exponents [11], unstable behavior of Hartley's oscillator because of the positive real parts of the eigenvalues of the Jacobian matrix of the system [12], and the global asymptotic stability (GAS) of the synchronization of Vilnius chaotic systems (using active and passive controls) determined by Lyapunov's direct method [13]. Moreover, some recent works have been done on the various behaviors of nonlinear RLC circuit systems: the existence of solutions [14], implicit solutions [15], power shaping [16], passivity and power-balance inequalities [17], and so on.…”

Section: Introductionmentioning

confidence: 99%

New results on the global asymptotic stability of certain nonlinear RLC circuits

Ateş¹,

Laribi²

2018

Turk J Elec Eng & Comp Sci

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This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit systems using the direct Lyapunov method. For each system a suitable Lyapunov function or energy-like function is constructed and the direct Lyapunov method is applied to the related system. Then the invariant equilibrium point of each system that makes the system solution to the global asymptotic stable is determined. Some new explicit GAS conditions of certain nonlinear RLC circuit systems are derived by Lyapunov's direct method. The presented simulations are compatible with the new results. The results are given with proofs.

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A minimum five‐component five‐term single‐nonlinearity chaotic jerk circuit based on a twin‐jerk single‐op‐amp technique

Munmuangsaen

Srisuchinwong

2017

Circuit Theory & Apps

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Summary A minimum 5‐component 5‐term single‐nonlinearity chaotic jerk circuit is presented as the first simplest chaotic jerk circuit in a category that a single op‐amp is employed. Such a simplest circuit displays 5 simultaneous advantages of (1) 5 minimum basic electronic components, (2) 5 minimum algebraic terms in a set of 3 coupled first‐order ordinary differential equations (ODEs), (3) a single minimum term of nonlinearity in the ODEs, (4) a simple passive component for nonlinearity, and (5) a single op‐amp. The proposed 5‐term single‐nonlinearity chaotic jerk circuit and a slightly modified version of an existing 6‐term 2‐nonlinearity chaotic jerk circuit form mirrored images of each other. Although both mirrored circuits yield 2 different sets of the ODEs, both sets however can be recast into a pair of twin jerk equations. Both mirrored circuits are therefore algebraically twin 5‐component chaotic jerk circuits, leading to a twin‐jerk single‐op‐amp approach to the proposed minimum chaotic jerk circuit. Two cross verifications of trajectories of both circuits are illustrated through numerical and experimental results. Dynamical properties are also presented.

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Hartley’s oscillator: The simplest chaotic two-component circuit

Cited by 68 publications

References 27 publications

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

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

New results on the global asymptotic stability of certain nonlinear RLC circuits

A minimum five‐component five‐term single‐nonlinearity chaotic jerk circuit based on a twin‐jerk single‐op‐amp technique

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