A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation

Xu, Ge Ning; Shekofteh, Yasser; Akgül, Akif; Li, Chunbiao; Panahi, Shirin

doi:10.3390/e20020086

Cited by 82 publications

(52 citation statements)

References 92 publications

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“…The fundamental motivation of this work is to show that structurally stable strange attractors can be observed in smooth dynamical system naturally considered as nonlinear but with non-chaotic limit sets. However, designed autonomous chaotic oscillators can serve as the core circuits in many practical applications such as cryptography [48], spread-spectrum modulation techniques [49], useful signal masking [50,51], random number generators [52,53], etc.…”

Section: Discussionmentioning

confidence: 99%

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

Petržela

2018

Entropy

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This paper brings analysis of the multiple-valued memory system (MVMS) composed by a pair of the resonant tunneling diodes (RTD). Ampere-voltage characteristic (AVC) of both diodes is approximated in operational voltage range as common in practice: by polynomial scalar function. Mathematical model of MVMS represents autonomous deterministic dynamical system with three degrees of freedom and smooth vector field. Based on the very recent results achieved for piecewise-linear MVMS numerical values of the parameters are calculated such that funnel and double spiral chaotic attractor is observed. Existence of such types of strange attractors is proved both numerically by using concept of the largest Lyapunov exponents (LLE) and experimentally by computer-aided simulation of designed lumped circuit using only commercially available active elements.

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Section: Discussionmentioning

confidence: 99%

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

Petržela

2018

Entropy

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“…In statistics, approximate entropy is a technique used to quantify the amount of regularity and unpredictability of uctuations over time series data. e main idea of approximate entropy is to use a nonnegative value to quantify the complexity and irregularity of the time series, and the value increases with increased sequence complexity [41][42][43]. Table 3 shows the results of the NIST test regarding the -values of the digitized chaotic time series from map (9) when = 12.…”

Section: Nonlinearity Complexity Analysismentioning

confidence: 99%

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Wang

Ding

2019

Complexity

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When chaotic systems are realized in digital circuits, their chaotic behavior will degenerate into short periodic behavior. Short periodic behavior brings hidden dangers to the application of digitized chaotic systems. In this paper, an approach based on the introduction of additional parameters to counteract the short periodic behavior of digitized chaotic time series is discussed. We analyze the ways that perturbation sources are introduced in parameters and variables and prove that the period of digitized chaotic time series generated by a digitized logistic map is improved e ciently. Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as a secure pseudorandom sequence generator for information encryption.

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“…Rather, an approximate entropy (ApEn) measure was proposed in [43,44]. ApEn has been used extensively in the literature to investigate chaos in discrete dynamical systems [25,45]. In order to examine the level of chaotic behavior present in the fractional map (6), we have measured its approximate entropy (ApEn) and listed it in Table 1.…”

Section: Entropy Analysismentioning

confidence: 99%

Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control

Ouannas

Wang

Khennaoui

et al. 2018

Entropy

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In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method.

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A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation

Cited by 82 publications

References 92 publications

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

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

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control

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