Two Element Chaotic and Hyperchaotic Circuits

Muthuswamy, Bharathwaj; Przybylski, Andrew; Feilbach, Chris; Mossbrucker, Joerg

doi:10.1007/978-3-642-33914-1_1

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…Though not yet as simple as the one proposed by Tchitnga et al (2008) where a tapped coil connected to a junction field effect transistor constitutes an autonomous chaos generator, the present circuit can be considered a ''two-component'' one in the sense of Pham et al (2013) or Muthuswamy et al (2012), however this is simpler if we consider the schematics of their nonlinear elements. These authors have proposed a circuit made of a capacitor in parallel with a time-delayed memristive element, respectively an inductor in parallel with a memristor.…”

Section: Resultsmentioning

confidence: 94%

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

Nanfa'a

Pelap

et al. 2016

Journal of Vibration and Control

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A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a ''two-component'' circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

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Section: Resultsmentioning

confidence: 94%

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

Nanfa'a

Pelap

et al. 2016

Journal of Vibration and Control

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“…This is due to the widespread usage of the most basic autonomous chaotic circuits in a variety of applications, including radar and sonar [1], secure chaotic communications [2], robotics [3], and random generator implementation [4]. The simplest autonomous chaotic oscillators have been identified in circuits from five up to two components [5][6][7][8][9][10][11][12][13][14]. Chaotic behaviors have been obtained in circuit made of a capacitor and a memristor [7].…”

Section: Introductionmentioning

confidence: 99%

“…The chaotic behavior of a two-component circuit consisting of a capacitor in parallel with a negative resistance as the nonlinear component has been demonstrated theoretically and practically. Using a nonlinear current-controlled meminductor, the authors of [6] proposed a two-element autonomous circuit. The autonomous chaotic jerk oscillators summarized by Sprott [15] and recently proposed in the literature [16][17][18][19][20][21][22][23][24][25][26] belong to the family of simplest autonomous chaotic oscillators.…”

Section: Introductionmentioning

confidence: 99%

Autonomous jerk oscillator with sine nonlinearity and logistic map for sEMG encryption

Ramakrishnan¹,

Welba²,

Cheage³

et al. 2022

Phys. Scr.

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The dynamical behaviors of the proposed autonomous jerk oscillator with sine nonlinearity (AJOSN) and its application to secure s-EMG (Surface ElectroMyoGraphic) data are discussed in this paper. The AJOSN has two or no-equilibrium points and the stability of the two equilibrium points shows that one of the equilibrium points is stable while the other is unstable. The AJOSN reveals fast-spiking and periodic bursting, relaxing and periodic oscillations, hidden chaotic attractors and coexisting attractors. The numerical analysis results are validated by the Field Programmable Gate Array (FPGA) implementation. Finally, the AJOSN's chaotic behavior coupled with the logistic map is exploited to encrypt the s-EMG signals. To improve security, the proposed encryption and decryption algorithm encrypts the s-EMG signal twice at the same time. After being converted to 2D in the form of a grayscale image, the s-EMG signal is encrypted for the first time using the chaotic signal generated by the AJOSN. The resulting encrypted signal is called to as "encrypted signal jerk." The chaotic logistics map is used to encrypt the final signal. The resulting encrypted signal is therefore the end product of the proposed encryption technique. The encryption and decryption results obtained are quite encouraging and offer a great prospect.

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Memristor: Models, Types, and Applications

Radwan

Fouda

2015

Studies in Systems, Decision and Control

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The first concept and realization of memory resistor device was proposed by Widrow in 1960 [1]. It was named memistor and had three terminals. The resistance of this memistor was variable and could be controlled and sensed using the control (DC current) and sensing (AC current) terminals. The significant difference between the transistor and the memistor is that the memistor resistance is controlled by the instantaneous time integral of the control current, which is the accumulated charge passing through the memistor. However, the memistor was not linked to the fundamentals of circuit theory because it is an "ill-posed" element, a 3-terminal device is said to be well posed if it has sufficient information to predict the current and voltage associated with all the three terminals when the device is connected to an arbitrary external circuit [2]. Moreover, in 1968, through the Electromagnetic theory, Fano et al. listed that there are four fundamental circuit elements: resistor, capacitor, inductor, and an unknown element [3].However, the first practical mathematical concept and realization was introduced by the father of nonlinear circuits, Prof. Leon Chua, in 1971 in his seminal paper

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Two Element Chaotic and Hyperchaotic Circuits

Cited by 5 publications

References 10 publications

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

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

Autonomous jerk oscillator with sine nonlinearity and logistic map for sEMG encryption

Memristor: Models, Types, and Applications

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