Detection of the chaotic behaviour of a bouncing ball by the 0–1 test

Litak, Grzegorz; Syta, Arkadiusz; Budhraja, Mridula; Saha, L. M.

doi:10.1016/j.chaos.2009.03.048

Cited by 32 publications

(16 citation statements)

References 22 publications

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“…It has been successfully applied to both numerically obtained [4][5][6][7][8] as well as to simple experimental data [9]. However, in a previous work [10] we have presented evidence that, when applied to time series stemming from nonhomogeneous, i.e dissimilar mass, many-degrees-offreedom systems, the test has serious limitations as an efficient chaos detector for a large system size N .…”

Section: Introductionmentioning

confidence: 99%

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

Romero-Bastida

Reyes-Martínez

2011

Phys. Rev. E

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In this work we study the possibility of detecting the so-called strong stochasticity threshold, i.e. the transition between weak and strong chaos as the energy density of the system is increased, in anharmonic oscillator chains by means of the 0-1 test for chaos. We compare the result of the aforementioned methodology with the scaling behavior of the largest Lyapunov exponent computed by means of tangent space dynamics, that has so far been the most reliable method available to detect the strong stochasticity threshold. We find that indeed the 0-1 test can perform the detection in the range of energy density values studied. Furthermore, we determined that conventional nonlinear time series analysis methods fail to properly compute the largest Lyapounov exponent even for very large data sets, whereas the computational effort of the 0-1 test remains the same in the whole range of values of the energy density considered with moderate size time series. Therefore, our results show that, for a qualitative probing of phase space, the 0-1 test can be an effective tool if its limitations are properly taken into account.

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Section: Introductionmentioning

confidence: 99%

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

Romero-Bastida

Reyes-Martínez

2011

Phys. Rev. E

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“…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%

“…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%

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 0/1 test (see [1][2][3][4][5][6][7][8][9][10][11][12][13] for details) is a relatively new tool used to test the presence of chaos in digital sequences when a mathematical model (system of equations) is not available.…”

Section: The 0/1 Test Fundamentalsmentioning

confidence: 99%

“…Also, a relative simplicity of the test and the binary nature of the final result -parameter K ≈ 1 for chaotic and K ≈ 0 for regular signals -made the test an attractive tool in examining signals and systems. Analysis of the properties of the 0/1 test and its interesting applications can also be found in [5][6][7][8][9]. While the 0/1 test for chaos can be applied to discrete and continuous signals, it appears (based on the literature) that the test is mostly used to examine discrete signals.…”

Section: Introductionmentioning

confidence: 99%

On the 0/1 test for chaos in continuous systems

Melosik¹,

Marszałek²

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In this paper we discuss in detail the resonance and oversampling features of the 0/1 test for chaos in continuous systems and propose methods to avoid those undesired features. Our method is based on certain frequency properties of the 0/1 test. When reconstructing the phase space, our approach is compared with the first minimum of the mutual information method. Several numerical results for typical chaotic systems (including memristive circuits) are included.Key words: test 0/1 for chaos, oversampling, phase space reconstruction, mutual information, FFT. Abstract. In this paper we discuss in detail the resonance and oversampling features of the 0/1 test for chaos in continuous systems and propose methods to avoid those undesired features. Our method is based on certain frequency properties of the 0/1 test. When reconstructing the phase space, our approach is compared with the first minimum of the mutual information method. Several numerical results for typical chaotic systems (including memristive circuits) are included. On the 0/1 test for chaos in continuous systems

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Detection of the chaotic behaviour of a bouncing ball by the 0–1 test

Cited by 32 publications

References 22 publications

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices

Hardware Trojans detection in chaos-based cryptography

On the 0/1 test for chaos in continuous systems

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