Assessing the chaos strength of Taylor approximations of the sine chaotic map

Kafetzis, Ioannis; Moysis, Lazaros; Volos, Christos

doi:10.1007/s11071-022-07929-y

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…The desirable result is that the number of floating point operations is reduced while maintaining complex dynamic structure as software implementation, and its implementation of the hardware circuit can become easier. The results of literature [28] show that in many cases, the dynamics of the maps defined using the Taylor approximation are more complex. Thus, this substitution should maintain the complex dynamic behavior of the original map.…”

Section: Processing For Transcendental Functions In the Map (1)mentioning

confidence: 99%

“…[30]. The modifications of these maps have been applied to PRNG designs and the PRNGs have successfully passed all statistical tests in the suite NIST SP 800-22 [28,31]. We predict that the use of Taylor expansions to approximate transcendental function terms in a chaotic map is a technical solution to the problems mentioned above.…”

Section: Introductionmentioning

confidence: 95%

“…For our research work, an important result from Ref. [28] is that the new polynomial map exhibits chaotic behavior (in many cases more complex) if the sine term of a original chaotic map is approximated by its Taylor expansion. The technique has been applied to enhance the sine map in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Modification of Intertwining Logistic Map and a Novel Pseudo Random Number Generator

Zhao,

2024

Symmetry

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Chaotic maps have been widely studied in the field of cryptography for their complex dynamics. However, chaos-based cryptosystems have not been widely used in practice. One important reason is that the following requirements of practical engineering applications are not taken into account: computational complexity and difficulty of hardware implementation. In this paper, based on the demand for information security applications, we modify the local structure of the three-dimensional Intertwining Logistic chaotic map to improve the efficiency of software calculation and reduce the cost of hardware implementation while maintaining the complex dynamic behavior of the original map. To achieve the goal by reducing the number of floating point operations, we design a mechanism that can be decomposed into two processes. One process is that the input parameters value of the original system is fixed to 2k by Scale index analysis. The other process is that the transcendental function of the original system is replaced by a nonlinear polynomial. We named the new map as “Simple intertwining logistic”. The basic chaotic dynamic behavior of the new system for controlling parameter is qualitatively analyzed by bifurcation diagram and Lyapunov exponent; the non-periodicity of the sequence generated by the new system is quantitatively evaluated by using Scale index technique based on continuous wavelet change. Fuzzy entropy (FuzzyEn) is used to evaluate the randomness of the new system in different finite precision digital systems. The analysis and evaluation results show that the optimized map could achieve the designed target. Then, a novel scheme for generating pseudo-random numbers is proposed based on new map. To ensure its usability in cryptographic applications, a series of analysis are carried out. They mainly include key space analysis, recurrence plots analysis, correlation analysis, information entropy, statistical complexity measure, and performance speed. The statistical properties of the proposed pseudo random number generator (PRNG) are tested with NIST SP800-22 and DIEHARD. The obtained results of analyzing and statistical software testing shows that, the proposed PRNG passed all these tests and have good randomness. In particular, the speed of generating random numbers is extremely rapid compared with existing chaotic PRNGs. Compared to the original chaotic map (using the same scheme of random number generation), the speed is increased by 1.5 times. Thus, the proposed PRNG can be used in the information security.

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Section: Processing For Transcendental Functions In the Map (1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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Modification of Intertwining Logistic Map and a Novel Pseudo Random Number Generator

Zhao,

2024

Symmetry

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“…We can generate the stability of an inverted pendulum by applying an external excitation. The excitation is in the form of an external oscillation that is applied to the pivot either in the horizontal [16][17][18][19][20][21][22] or the vertical [23][24][25][26][27][28][29][30][31][32][33] direction.…”

Section: Modelingmentioning

confidence: 99%

“…Just as additional information, the problems of the inverted pendulum subjected to vertical excitation have been widely discussed [23][24][25][26][27][28][29][30][31][32][33]. For small deviation angles, the basic equation is Mathieu's equation which can be written as d 2 θ dt 2 + k (1 − m cos ωt) θ = 0 with k = g/Lω 2 , m = a/L, a is the amplitude of the pivot oscillation, L is the length of the pendulum, and ω is the excitation frequency [34].…”

Section: Modelingmentioning

confidence: 99%

Traditional stilts as an alternating incomplete inverted pendulum controlled by hand and a physical pendulum pivoting at the hand

Akbar¹,

Khalifah²,

Abdullah³

2021

Eur. J. Phys.

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Traditional stilts have been known in many countries in Asia and Africa and are generally used as toys. The design is very simple, but their use is very difficult. Performers have to train intensively to control their stability so they can walk using them. An interesting challenge is what kind of physical formulation controls the stability of traditional stilts. In this paper, we report a simple physical formulation to explain the mechanics of traditional stilts. The traditional stilts can be considered as an alternating inverted pendulum stabilized by hand and a physical pendulum pivoting at the hand. Experiments were also carried out using a stilt made of bamboo rods. We identified a number of parameters that control the stability of the stilts. This type of research can become a topic for research-based learning at universities.

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Bifurcations in a new two-cell spiking map: a numerical and experimental study

Buscarino,

Famoso,

Fortuna

2023

Nonlinear Dyn

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In this paper, a new nonlinear discrete-time map is presented. The map is based on a second-order dynamics that, despite the limited number of parameters, is able to produce a rich dynamical behavior, including the onset of spiking trends. This latter case will be particularly emphasized, since it allows to consider the introduced system as a novel discrete-time model for spiking neurons. The study is performed by using a numerical bifurcation approach. Moreover, the possibility to obtain a spiking behavior using noise is also shown. The implementation of the map using advanced microcontroller units and the obtained experimental results are discussed.

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Assessing the chaos strength of Taylor approximations of the sine chaotic map

Cited by 6 publications

References 40 publications

Modification of Intertwining Logistic Map and a Novel Pseudo Random Number Generator

Modification of Intertwining Logistic Map and a Novel Pseudo Random Number Generator

Traditional stilts as an alternating incomplete inverted pendulum controlled by hand and a physical pendulum pivoting at the hand

Bifurcations in a new two-cell spiking map: a numerical and experimental study

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