On the 0/1 test for chaos in continuous systems

Melosik, Michał; Marszałek, Wiesław

doi:10.1515/bpasts-2016-0058

Cited by 17 publications

(41 citation statements)

References 19 publications

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“…However, some abating factors must be addressed. The test will always return a periodic diagnosis when the data is over-sampled for the case of time-continuous systems [10]. Additionally, false positives are found when periodic time series are contaminated with substantial noise [5].…”

Section: The Traditional 0-1 Testmentioning

confidence: 99%

“…Additionally, false positives are found when periodic time series are contaminated with substantial noise [5]. The issue of oversampling can be resolved by properly sub-sampling the time series according to [10,11,12], the effects of noise are more difficult to overcome. A method has been developed which allows the 0-1 test to handle noise very effectively if a gauge-value (i.e.…”

Section: The Traditional 0-1 Testmentioning

confidence: 99%

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A look into chaos detection through topological data analysis

Tempelman

Khasawneh

2020

Physica D: Nonlinear Phenomena

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Traditionally, computation of Lyapunov exponents has been the marque method for identifying chaos in a time series. Recently, new methods have emerged for systems with both known and unknown models to produce a definitive 0-1 diagnostic. However, there still lacks a method which can reliably perform an evaluation for noisy time series with no known model. In this paper, we present a new chaos detection method which utilizes tools from topological data analysis. Bi-variate density estimates of the randomly projected time series in the p-q plane described in Gottwald and Melbourne's approach for 0-1 detection are used to generate a gray-scale image. We show that simple statistical summaries of the 0D sub-level set persistence of the images can elucidate whether or not the underlying time series is chaotic. Case studies on the Lorenz and Rossler attractors as well as the Logistic Map are used to validate this claim. We demonstrate that our test is comparable to the 0-1 correlation test for clean time series and that it is able to distinguish between periodic and chaotic dynamics even at high noise-levels. However, we show that neither our persistence based test nor the 0-1 test converge for trajectories with partially predicable chaos, i.e. trajectories with a cross-distance scaling exponent of zero and a non-zero cross correlation.

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Section: The Traditional 0-1 Testmentioning

confidence: 99%

Section: The Traditional 0-1 Testmentioning

confidence: 99%

A look into chaos detection through topological data analysis

Tempelman

Khasawneh

2020

Physica D: Nonlinear Phenomena

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“…The 0-1 test (see [16][17][18][19][20][21][22][23][24][25] for details) is a relatively new tool used to test the presence of chaos in analog and digital sequences when a mathematical model (system of equations) is not available. The result of the test has two forms: a single real number K, and a two-dimensional graph with translation variables p c and q c [16,17].…”

Section: Chaos Detecting 0-1 Testmentioning

confidence: 99%

“…Finally, the median of the N c values of K c is the final number K. The K ¼ 1 indicates a chaotic sequence, while K ¼ 0 indicates regular (non-chaotic) dynamics. For more details about the 0/1 test, its properties and reliability in the continuous and discrete cases one can see [18][19][20][21][22][23][24][25].…”

Section: Hts In Lindberg's Generatormentioning

confidence: 99%

Hardware Trojans detection in chaos-based cryptography

Melosik

Śniatała

Marszałek

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The paper deals with the security problems in chaotic-based cryptography. In particular, the 0-1 test for chaos is used to detect hardware Trojans in electronic circuits -generators of chaotic bit sequences. The proposed method of detecting hardware Trojans is based on analyzing the original bit sequences through the 0-1 test yielding a simple result, either a number close to 1, when the examined bit sequence is chaotic, or a number close to 0, when the sequence is non-chaotic. A complementary result is a graph of translation variables q c and p c which form a basis of the 0-1 test. The method does not require any extra corrections and can be applied to relatively short sequences of bits. This makes the method quite attractive as the security problems are dealt with at the chaotic generator level, with no need to apply any extractors of randomness. The method is illustrated by numerical examples of simulated Trojans in chaotic bit generators based on the analog Lindberg circuit as well as a discrete system based on the logistic map.Key words: chaos-based cryptography, hardware Trojans, 0-1 test for chaos, bit generators. sequences is to use chaotic circuits. Such an approach is straightforward when compared to the use of quantum modules, which require significantly larger areas on PCBs. A random sequence generator can be integrated with a security module or it can itself be a separate module. The security issues of embedded systems, such as PCBs, were first discussed in [6]. However, [6] does not discuss the security problems and hardware Trojan attacks on random sequence generators based on chaotic circuits. This paper deals with such problems based on testing of chaotic signals by the 0-1 test for chaos. The result of such test is two-fold: a single number, close to either 0 or 1, and a visual two-dimensional plot of the so-called translation variables q c and p c , that in future might be implemented online in real time. Hardware Trojans detection in chaos-based cryptographyAs discussed in [6][7][8][9][10], the security issues and protection against HTs is a key problem in modern electronics and computer engineering. In this paper we discuss HTs that may easily be implemented and integrated with the PCB modules in chaotic analog generators. We also discuss HTs implemented through FPGA in chaotic discrete generators.

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“…The mathematical background can be found in the article by Gottwald and Melbourne, Bernardini and Litak, or in the latest review . This test is applicable on discrete dynamical systems, continuous dynamical systems, and on real data represented as time series . This test has been successfully used in many applications, for example, in distinguishing between chaos and randomness from a noisy data, exploration of mechanical system's dynamic properties consisting of a ball jumping between a movable baseplate and a fixed upper stop .…”

Section: Introductionmentioning

confidence: 99%

Dynamical properties of the improved FK3V heart cell model

Halfar

Lampart

2018

Math Methods in App Sciences

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The main aim of this paper is to study the evolution of the transmembrane potential on the cardiac cell under different rates and amplitudes of stimulation. For modeling this potential, the modification of the Fenton‐Karma model was applied. It is a phenomenological model with 3 degrees of freedom that corresponds to nondimensional transmembrane potential and gating variables for regulation of inward and outward ion currents that can better reproduce the shape of the transmembrane potential than the original Fenton‐Karma model. The model was newly forced by stimulus with the shape of the half‐sine period. As the main goal of the paper is to show that this model is showing regular as well as irregular motion; periodic and chaotic patterns are detected using bifurcation diagrams, the Fourier spectra, Poincaré sections, and 0‐1 test for chaos.

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On the 0/1 test for chaos in continuous systems

Cited by 17 publications

References 19 publications

A look into chaos detection through topological data analysis

A look into chaos detection through topological data analysis

Hardware Trojans detection in chaos-based cryptography

Dynamical properties of the improved FK3V heart cell model

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