Strange Attractors Generated by Multiple-Valued Static Memory Cell with Polynomial Approximation of Resonant Tunneling Diodes

Petržela, Jiří

doi:10.3390/e20090697

Cited by 22 publications

(12 citation statements)

References 47 publications

(58 reference statements)

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“…Previous researches have described general methods in order to implement mathematical models using voltage-mode devices [42] and current-mode active elements [10]. It is possible to implement the forced chaotic oscillator (6) by using a circuit [43][44][45][46][47][48][49][50][51] as designed in Fig. 8.…”

Section: Circuit Designmentioning

confidence: 99%

A Novel Mega-stable Chaotic Circuit

Pham¹,

Ali²,

Al-Saidi³

et al. 2020

RADIOENGINEERING

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In recent years designing new multistable chaotic oscillators has been of noticeable interest. A multistable system is a double-edged sword which can have many benefits in some applications while in some other situations they can be even dangerous. In this paper, we introduce a new multistable two-dimensional oscillator. The forced version of this new oscillator can exhibit chaotic solutions which makes it much more exciting. Also, another scarce feature of this system is the complex basins of attraction for the infinite coexisting attractors. Some initial conditions can escape the whirlpools of nearby attractors and settle down in faraway destinations. The dynamical properties of this new system are investigated by the help of equilibria analysis, bifurcation diagram, Lyapunov exponents' spectrum, and the plot of basins of attraction. The feasibility of the proposed system is also verified through circuit implementation.

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Section: Circuit Designmentioning

confidence: 99%

A Novel Mega-stable Chaotic Circuit

Pham¹,

Ali²,

Al-Saidi³

et al. 2020

RADIOENGINEERING

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“…Quite recently, it has been proved that robust chaotic waveforms can be generated by binary memory composed by two coupled resonant tunneling diodes (RTD) [39] approximated by either piecewise linear (PWL) [40] or cubic polynomial function [41]. Both diodes possess typical N-type ampere-voltage characteristics (AVC) and three degrees of freedom required for chaos evolution are obtained due to the parasitic features of RTDs observed on the high frequencies.…”

Section: Wideband Cpe As Part Of Chaotic Systemmentioning

confidence: 99%

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Petržela

2020

Entropy

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This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement.

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“…Unexpected chaotic response was reported in fundamental configuration of a phase-locked loop [68], [69] which is standard radio-frequency functional block. Traces of chaos were discovered in the logic gates [70] as well as in the different conceptions of the multiple-valued static memory cell; both with piecewise-linear [71] and polynomial [72] approximation of the resonant tunneling diodes. Here, we can find direct connection between number of the stable states and complexity of the chaotic attractors.…”

Section: Introductionmentioning

confidence: 99%

Minimal Realizations of Autonomous Chaotic Oscillators Based on Trans-Immittance Filters

Petržela

Polák

2019

IEEE Access

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This review paper describes a design process toward fully analog realizations of chaotic dynamics that can be considered canonical (minimum number of the circuit elements), robust (exhibit structurally stable strange attractors), and novel. Each autonomous chaotic lumped circuit proposed in this paper can be understood as a looped system, where linear trans-immittance frequency filter interacts with an active nonlinear two-port. The existence of chaos is demonstrated via well-established numerical algorithms that represent the current standard in the field of nonlinear dynamics, i.e., by calculation of the largest Lyapunov exponent and high-resolution 1-D bifurcation diagrams. The achieved numerical results are put into the context of experimental measurement; observed state trajectories prove a one-to-one correspondence between theoretical expectations and practical outputs, i.e., prescribed strange attractors do not represent the chaotic transients. Finally, short term unpredictability of the chaotic flow is demonstrated via calculation of Kaplan-Yorke dimension that is high, i.e., generated waveforms can find interesting applications in the fields of chaotic masking, modulation, or chaos-based cryptography.

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Strange Attractors Generated by Multiple-Valued Static Memory Cell with Polynomial Approximation of Resonant Tunneling Diodes

Cited by 22 publications

References 47 publications

A Novel Mega-stable Chaotic Circuit

A Novel Mega-stable Chaotic Circuit

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Minimal Realizations of Autonomous Chaotic Oscillators Based on Trans-Immittance Filters

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