Simple Chaotic Circuit Using Cmos Ring Oscillators

Hosokawa, Yasuteru; Nishio, Yoshifumi

doi:10.1142/s0218127404010795

Cited by 17 publications

(19 citation statements)

References 5 publications

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“…For example, they often provide the frequency standard for phase lock loop control systems, with frequencies typically in the megahertz range. Recently, ring oscillators have been connected by diodes to create a chaotic circuit [11]. At the nodes that connect the output of one inverter to the input of the next inverter, we insert a capacitor in series with bi-directional bi-colored light-emitting diodes (LEDs) to ground.…”

Section: Mechanical Reverser Arraymentioning

confidence: 99%

Electronic and mechanical realizations of one-way coupling in one and two dimensions

et al. 2011

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One-way or unidirectional coupling is a striking example of how topological considerations--the parity of an array of multistable elements combined with periodic boundary conditions--can qualitatively influence dynamics. Here we introduce a simple electronic model of one-way coupling in one and two dimensions and experimentally compare it to an improved mechanical model and an ideal mathematical model. In two dimensions, computation and experiment reveal richer one-way coupling phenomenology: in media where two-way coupling would dissipate all excitations, one-way coupling enables solitonlike waves to propagate in different directions with different speeds.

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Section: Mechanical Reverser Arraymentioning

confidence: 99%

Electronic and mechanical realizations of one-way coupling in one and two dimensions

et al. 2011

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“…An electrical implementation of most of the scientific study comes with conventional operational amplifier (Op-Amp) with excess number of passive components with large chip area, high power dissipation in comparison to advance analogue building block in chaotic circuits [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. However, a monolithic implementation of canonical mathematical model for generation of chaotic waveform using commercially available components as well as complementary metal oxide semiconductor (CMOS)-based operational transconductance amplifier (OTA) with comparator [13] and inverter [14] are well depicted.…”

Section: Introductionmentioning

confidence: 99%

Dual feedback IRC ring for chaotic waveform generation

Joshi

Ranjan

2021

IET Circuits, Devices & Systems

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The authors have proposed an inverter resistor capacitor (IRC)-based simple chaotic ring oscillator with dual feedback for the generation of the chaotic waveform. The proposed chaotic system uses three coupled autonomous first-order differential equations and it can be electrically demonstrated using the complementary metal oxide semiconductor (CMOS) inverters with few passive RC elements for the generation of the high-frequency strange attractor. The basic dynamical characteristics and multistability property with complex bifurcation pattern in a wide range of parameters are well observed through theoretical as well as numerical simulation analysis using scaled inverse tangent function. In addition, a simple IRC chaotic model design is investigated using 0.18μm MOS transistor parameters with grounded capacitors and an equivalent CMOS-based scaled inverse tangent function. Moreover, the Cadence post layout simulation gives useful information about the circuit sustainability for IC design with high frequency (MHz), low power dissipation (940 μW) and small chip area (826.3 μm 2). This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…One encounters difficulties when one conducts Lyapunov analysis using exact solutions of piecewise linear differential equations because it usually requires tremendous manual calculations. Hosokawa and Nishio obtained the largest Lyapunov exponent of a circuit of which governing equation is represented by a sixdimensional differential equation [19]. First of all, they have to numerically solve the eigenvalue equation since the explicit formula does not exist for five-or higher-algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the task deriving all Lyapunov exponents is extremely troublesome and is not realizable. In [19], only the largest Lyapunov exponent was derived.…”

Section: Introductionmentioning

confidence: 99%

Numerical sensitivity in the analysis of a high-dimensional oscillator

Inaba

Sekikawa

Endo

2012

NOLTA

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We have encountered serious difficulties when we analyze bifurcation phenomena in a high-dimensional oscillator by Lyapunov analysis. Our model uses an eight-dimensional piecewise-linear oscillator containing a hysteresis element. The numerical results show that the solutions do not arrive at a stationary state quite often even if we use piecewise-linear exact solutions and remove more than 100,000 transient iteration of the Poincaré map. Furthermore, we calculate the Lyapunov exponents by averaging 1,000,000 iteration of the Jacobian matrix of the Poincaré map after removing transient 500,000 iteration. The values of the Lyapunov exponents themselves could be trustworthy because piecewise-linear exact solutions have been employed. However, it is very difficult to classify the solutions from the value of the calculated Lyapunov exponents even if the attractor is not chaotic. This is because the bifurcation structure of a higher-dimensional torus is extremely complicated. In some cases, it is very hard to settle how many iteration is necessary to calculate reasonable Lyapunov exponents, and to distinguish whether Lyapunov exponents are exactly zero or not from the values of the numerically calculated Lyapunov exponents. This is a major concern of this study. These complex situations are spotlighted by observing attractors and drawing the graph of the Lyapunov exponents.

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Simple Chaotic Circuit Using Cmos Ring Oscillators

Cited by 17 publications

References 5 publications

Electronic and mechanical realizations of one-way coupling in one and two dimensions

Electronic and mechanical realizations of one-way coupling in one and two dimensions

Dual feedback IRC ring for chaotic waveform generation

Numerical sensitivity in the analysis of a high-dimensional oscillator

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